what is the value that occurs most frequently in a distribution
Mode
4495867
In symbols, where formula_7 is the absolute value. A similar relation holds between the median and the mode: they lie within 3 ≈ 1.732 standard deviations of each other: The term mode originates with Karl Pearson in 1895. Mode (statistics) The mode of a set of data values is the value that appears most often. It is the value "x" at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually)
Mode (statistics)
4495856
highly skewed distributions. The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points "x", "x", etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently. When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution. Such a continuous distribution is called multimodal (as opposed to unimodal). A mode of a continuous probability distribution is often considered to be any value "x"
Mode (statistics)
2762372
remaining variables is then effectively a posterior distribution conditioned on the observed data. The most likely value of a desired parameter (the mode) could then simply be selected by choosing the sample value that occurs most commonly; this is essentially equivalent to maximum a posteriori estimation of a parameter. (Since the parameters are usually continuous, it is often necessary to "bin" the sampled values into one of a finite number of ranges or "bins" in order to get a meaningful estimate of the mode.) More commonly, however, the expected value (mean or average) of the sampled values is chosen; this
Gibbs sampling
4495857
at which its probability density function has a locally maximum value, so any peak is a mode. In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide. For samples, if it is known that they are drawn from a symmetric unimodal distribution, the sample mean can be used as an estimate of the population mode. The mode of a sample is the element that occurs most often in the collection. For example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the
Mode (statistics)
2762373
is a Bayes estimator that takes advantage of the additional data about the entire distribution that is available from Bayesian sampling, whereas a maximization algorithm such as expectation maximization (EM) is capable of only returning a single point from the distribution. For example, for a unimodal distribution the mean (expected value) is usually similar to the mode (most common value), but if the distribution is skewed in one direction, the mean will be moved in that direction, which effectively accounts for the extra probability mass in that direction. (Note, however, that if a distribution is multimodal, the expected value may
Gibbs sampling
15739182
present values of operating profit and launch costs. Fig. 3. As described, a range is an estimate of a maximum, most-likely (or mode) and minimum (or Optimistic, Most-Likely, Pessimistic) values that circumscribe a triangular distribution. The two distributions are then combined, and, similar to the approach for simulation described, the expected value is the first moment of all positive NPVs. Here, using equations from triangular distributions, the mean of the launch cost distribution is calculated. The present value imputed net profit distribution is the difference between the operating profit distribution and the mean value of the launch cost distribution. In
Datar–Mathews method for real option valuation
1660433
list of mode cases, for arbitrary values of "α" and "β". For several of these cases, the maximum value of the density function occurs at one or both ends. In some cases the (maximum) value of the density function occurring at the end is finite. For example, in the case of "α" = 2, "β" = 1 (or "α" = 1, "β" = 2), the density function becomes a right-triangle distribution which is finite at both ends. In several other cases there is a singularity at one end, where the value of the density function approaches infinity. For example, in
Beta distribution
502154
In a long-channel device, there is no drain voltage dependence of the current once formula_19, but as channel length is reduced drain-induced barrier lowering introduces drain voltage dependence that depends in a complex way upon the device geometry (for example, the channel doping, the junction doping and so on). Frequently, threshold voltage "V" for this mode is defined as the gate voltage at which a selected value of current "I" occurs, for example, "I" = 1μA, which may not be the same "V"-value used in the equations for the following modes. Some micropower analog circuits are designed to take advantage
MOSFET
4495855
Mode (statistics) The mode of a set of data values is the value that appears most often. It is the value "x" at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in
Mode (statistics)
128440
namely the true value divided by the asymptotic value of the estimator. This occurs frequently in estimation of scale parameters by measures of statistical dispersion. An asymptotically normal estimator is a consistent estimator whose distribution around the true parameter "θ" approaches a normal distribution with standard deviation shrinking in proportion to formula_38 as the sample size "n" grows. Using formula_39 to denote convergence in distribution, "t" is asymptotically normal if for some "V". In this formulation "V/n" can be called the "asymptotic variance" of the estimator. However, some authors also call "V" the "asymptotic variance". Note that convergence will not
Estimator
50903
occurs frequently in pure and applied mathematics, economics and physics. The Wiener process "W" is characterized by four facts: formula_40 denotes the normal distribution with expected value "μ" and variance "σ". The condition that it has independent increments means that if formula_41 then formula_42 and formula_43 are independent random variables. An alternative characterisation of the Wiener process is the so-called "Lévy characterisation" that says that the Wiener process is an almost surely continuous martingale with "W" = 0 and quadratic variation formula_44. A third characterisation is that the Wiener process has a spectral representation as a sine series whose coefficients
Brownian motion
17274316
Symmetric probability distribution In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function or probability mass function is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution. Thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value. A probability distribution is said to
Symmetric probability distribution
1790645
acting occurs when the sex worker is aware of the dissonance between their authentic experience of emotion and their managed emotional display. In contrast deep acting occurs when the sex worker can no longer differentiate between what is authentic and what is acting; acting becomes authentic. Sex workers engage in emotional labor for many different reasons. First, sex workers often engage in emotional labor to construct performances of gender and sexuality. These performances frequently reflect the desires of a clientele which is mostly composed of heterosexual men. In the majority of cases, clients value women who they perceive as normatively
Sex work
7200863
or is nonexistent among most Tibeto-Burman-speaking populations of Southwest China, Northeast India, and Nepal, who exhibit extremely high frequencies of O-M117. This paragroup also occurs with very low frequency or is non-existent among most Mon-Khmer population of Laos, who exhibit much higher frequencies of O-M117 . In Han Chinese, the paragroup is found in approximately the same percentage as O-M117, but has a higher distribution in northern Han Chinese than Southern Han Chinese . Haplogroup O2a2b1a1-M117 (also defined by the phylogenetically equivalent mutation Page23) is a subclade of O2a2b1-M134 that occurs frequently in China and in neighboring countries, especially among
Haplogroup O-M122
2296780
with zero mean: Then the Wishart distribution is the probability distribution of the random matrix known as the scatter matrix. One indicates that has that probability distribution by writing The positive integer is the number of "degrees of freedom". Sometimes this is written . For the matrix is invertible with probability if is invertible. If then this distribution is a chi-squared distribution with degrees of freedom. The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution. It occurs frequently in likelihood-ratio tests in multivariate statistical analysis. It also arises in
Wishart distribution
11573695
to generate a Tukey lambda PPCC plot of a data set. Based on the PPCC plot, an appropriate model for the data is suggested. For example, if the maximum correlation occurs for a value of "λ" at or near 0.14, then the data can be modeled with a normal distribution. Values of "λ" less than this imply a heavy-tailed distribution (with −1 approximating a Cauchy). That is, as the optimal value of lambda goes from 0.14 to −1, increasingly heavy tails are implied. Similarly, as the optimal value of "λ" becomes greater than 0.14, shorter tails are implied. Since the
Tukey lambda distribution
1660482
distribution). What really matters is the relative value of entropy. Given two beta distributed random variables, "X" ~ Beta("α", "β") and "X" ~ Beta("α"′, "β"′), the cross entropy is (measured in nats) The cross entropy has been used as an error metric to measure the distance between two hypotheses. Its absolute value is minimum when the two distributions are identical. It is the information measure most closely related to the log maximum likelihood (see section on "Parameter estimation. Maximum likelihood estimation")). The relative entropy, or Kullback–Leibler divergence "D"("X", "X"), is a measure of the inefficiency of assuming that the distribution
Beta distribution
2117873
null hypothesis is rejected if the "F" calculated from the data is greater than the critical value of the "F"-distribution for some desired false-rejection probability (e.g. 0.05). The "F"-test is a Wald test. F-test An "F"-test is any statistical test in which the test statistic has an "F"-distribution under the null hypothesis. It is most often used but this occurs when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact ""F"-tests" mainly arise when the models have been fitted to
F-test
2175670
null hypothesis. The quantity "X" has the same distribution in Bayesian statistics, if an uninformative rescaling-invariant Jeffreys prior is taken for the prior probabilities of σ and σ. In this context, a scaled "F"-distribution thus gives the posterior probability "p"(σ/σ|"s", "s"), where now the observed sums "s" and "s" are what are taken as known. F-distribution In probability theory and statistics, the "F"-distribution, also known as Snedecor's "F" distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the
F-distribution
386984
an atomic or molecular resonance, the spectral line shape function is described as a Lorentzian distribution where formula_12 is the full width at half maximum or FWHM bandwidth. The peak value of the Lorentzian line shape occurs at the line center, formula_13. A line shape function can be normalized so that its value at formula_9 is unity; in the case of a Lorentzian we obtain Thus stimulated emission at frequencies away from formula_9 is reduced by this factor. In practice there may also be broadening of the line shape due to inhomogeneous broadening, most notably due to the Doppler effect
Stimulated emission
6533667
(M4) can be estimated if one partner knows the difference in lengths between the two most different suits (M2). This works because M2 is almost always approximately 75 percent of M4, meaning that M4 can be estimated by increasing M2 by 1/3. Keep in mind that this estimate will slightly under-value the hand in the case of "freak" distribution (where M4 is greater than 14) because M2 is only 60 percent of M4 for such wild distribution. This only occurs 0.8 percent of the time. To improve the accuracy of the point count, standard "judgment" adjustments can be used, such
Zar Points
3854479
as distinct from the theoretical value in an idealized distribution. One does not actually know that a certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years. This distinction is significant because there are few observations of rare events: for instance if observations go back 400 years, the most extreme event (a 400-year event by the statistical definition) may later be classed, on longer observation, as a 200-year event (if a comparable event immediately occurs) or a 500-year event (if no comparable event occurs for a further 100 years). Further, one
Return period
4421684
population which gradually "tails off" asymptotically. The events at the far end of the tail have a very low probability of occurrence. As a rule of thumb, for such population distributions the majority of occurrences (more than half, and where the Pareto principle applies, 80%) are accounted for by the first 20% of items in the distribution. What is unusual about a long-tailed distribution is that the most frequently occurring 20% of items represent less than 50% of occurrences; or in other words, the least frequently occurring 80% of items are more important as a proportion of the total population.
Long tail
9285200
colors is the same as the distribution over tables in the Chinese restaurant process. Furthermore, when we draw a black ball, if rather than generating a new color, we instead pick a random value from a base distribution formula_1 and use that value to label the new ball, the resulting distribution over labels will be the same as the distribution over values in a Dirichlet process. Dirichlet processes are frequently used in "Bayesian nonparametric statistics". "Nonparametric" here does not mean a parameter-less model, rather a model in which representations grow as more data are observed. Bayesian nonparametric models have gained
Dirichlet process
612375
of the maximum can be derived: The associated indicator function formula_4 is a Bernoulli process with a success probability formula_5 that depends on the magnitude formula_6 of the extreme event. The number of extreme events within formula_7 trials thus follows a binomial distribution and the number of trials until an event occurs follows a geometric distribution with expected value and standard deviation of the same order formula_8. In practice, we might not have the distribution function formula_9 but the Fisher–Tippett–Gnedenko theorem provides an asymptotic result. If there exist sequences of constants formula_10 and formula_11 such that as formula_13 then where
Extreme value theory
978795
the degenerate distribution is localized at a point "k" on the real line. The probability mass function equals 1 at this point and 0 elsewhere. The degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta function at "k", with infinite height there but area equal to 1. The cumulative distribution function of the univariate degenerate distribution is: formula_1 In probability theory, a constant random variable is a discrete random variable that takes a constant value, regardless of any event that occurs.
Degenerate distribution
5527408
parts of its range, the species has a wide distribution, large population, occurs in a number of protected areas, and it is unlikely to be declining at nearly the rate required to qualify for listing in a threatened category". Wombats were hunted by aboriginal people for their meat. However, capturing a wombat takes considerable time and energy, so they were not hunted too frequently. The indigenous people of Australia value the wombat culturally and keep their local wombat populations healthy by hunting wombats in other areas. Wombats have been considered as agricultural pests by landholders. Their digging can destroy crops
Southern hairy-nosed wombat
1633036
as far east as the Urals, whereas the most western population is that of Portugal. Breeding also occurs in northern Africa, mostly in Morocco. In Great Britain, the species is limited to southern England. In Ireland the species is rarely seen, and mainly in the South, although there are a number of breeding records, the most recent from 1971. Despite having a wide distribution, this bird is not common in many areas and has strong populations only in France, Spain, Russia, Belarus and Poland where the greater part of the European population can be found. Breeding sites frequently change, with
Montagu's harrier
3213233
one term common to both premises. In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation: using the same word or phrase but with a different meaning each time, creating a fourth term even though only three distinct words are used: The word "nothing" in the example above has two meanings, as presented: "nothing is better" means the thing being named has the highest value possible; "better than nothing" only means that the thing being described has some value. Therefore, "nothing" acts as two different terms in this example, thus creating the fallacy of four terms. Another
Fallacy of four terms
14648606
the average (usually, arithmetic mean) of the distributions. So the highest value in all cases becomes the mean of the highest values, the second highest value becomes the mean of the second highest values, and so on. Generally a reference distribution will be one of the standard statistical distributions such as the Gaussian distribution or the Poisson distribution. The reference distribution can be generated randomly or from taking regular samples from the cumulative distribution function of the distribution. However, any reference distribution can be used. Quantile normalization is frequently used in microarray data analysis. It was introduced as quantile standardization
Quantile normalization
16248083
Salix hastata Salix hastata is a species of flowering plant in the willow family, known by the common name halberd willow. It has an "almost circumpolar" distribution, occurring throughout the northern latitudes of the Northern Hemisphere, most frequently found near the coast of the Arctic Ocean. In Alaska, it occurs in the north and in the central mountains. It also occurs in northwestern Canada, and in Norway and Russia, as well as various alpine or mountainous areas of Eurasia. The specific epithet "hastata" means "spear-shaped". This willow varies widely in appearance, depending on environmental conditions. In general, it is a
Salix hastata
20252231
PERT distribution where formula_1 formula_2 (the incomplete beta function) with formula_4 In probability and statistics, the PERT distribution is a family of continuous probability distributions defined by the minimum (a), most likely (b) and maximum (c) values that a variable can take. It is a transformation of the four-parameter Beta distribution with an additional assumption that its expected value is The mean of the distribution is therefore defined as the weighted average of the minimum, most likely and maximum values that the variable may take, with four times the weight applied to the most likely value. This assumption about the
PERT distribution
7521318
Chi-squared target models Swerling models were introduced by Peter Swerling and are used to describe the statistical properties of the radar cross-section of complex objects. Swerling target models give the radar cross-section (RCS) of a given object using a distribution in the location-scale family of the chi-squared distribution. where formula_2 refers to the mean value of formula_3. This is not always easy to determine, as certain objects may be viewed the most frequently from a limited range of angles. For instance, a sea-based radar system is most likely to view a ship from the side, the front, and the back,
Chi-squared target models
2658050
by formula_7 and integrating over formula_5. This allows us to combine the logarithms yielding This is a quasi-KL divergence ("quasi" in the sense that the square root of the Fisher information may be the kernel of an improper distribution). Due to the minus sign, we need to minimise this in order to maximise the KL divergence with which we started. The minimum value of the last equation occurs where the two distributions in the logarithm argument, improper or not, do not diverge. This in turn occurs when the prior distribution is proportional to the square root of the Fisher information
Prior probability
16468251
proposed that use either the z or t distributions to determine significance, and each estimates the standard error differently. The distribution of the product term αβ is only normal at large sample sizes which means that at smaller sample sizes the p-value that is derived from the formula will not be an accurate estimate of the true p-value. This occurs because both "α" and "β" are assumed to be normally distributed, and the distribution of the product of two normally distributed variables is skewed, unless the means are much larger than the standard deviations. If the sample is large enough
Sobel test
3991542
protection in the structure of the deal. The most common form of credit protection is called credit tranching. In the simplest case, credit tranching means that any credit losses will be absorbed by the most junior class of bondholders until the principal value of their investment reaches zero. If this occurs, the next class of bonds absorb credit losses, and so forth, until finally the senior bonds begin to experience losses. More frequently, a deal is embedded with certain "triggers" related to quantities of delinquencies or defaults in the loans backing the mortgage pool. If a balance of delinquent loans
Collateralized mortgage obligation
2344434
of their CPU, FSB, GPU and RAM. Typically the programmable clock generator is set by the BIOS at boot time to the selected value; although some systems have dynamic frequency scaling, which frequently re-programs the clock generator. TSGs are clocks that are used throughout service-provider networks, frequently as the building integrated timing supply (BITS) for a central office. Digital switching systems and some transmission systems (e.g., SONET) depend on reliable, high-quality synchronization (or timing) to prevent impairments. To provide this, most service providers utilize interoffice synchronization distribution networks based on the stratum hierarchy and implement the BITS concept to meet
Clock generator
1497834
of the individual links, it is easily shown that Notice this last result is the same as that found for random walks in time. Assuming, as stated, that that distribution of end-to-end vectors for a very large number of identical polymer chains is gaussian, the probability distribution has the following form What use is this to us? Recall that according to the principle of equally likely "a priori" probabilities, the number of microstates, Ω, at some physical value is directly proportional to the probability distribution at that physical value, "viz"; where "c" is an arbitrary proportionality constant. Given our distribution
Polymer physics
13375546
nominal coverage probability, the interval is termed "anti-conservative", or "permissive." A discrepancy between the coverage probability and the nominal coverage probability frequently occurs when approximating a discrete distribution with a continuous one. The construction of binomial confidence intervals is a classic example where coverage probabilities rarely equal nominal levels. For the binomial case, several techniques for constructing intervals have been created. The Wilson or Score confidence interval is one well known construction based on the normal distribution. Other constructions include the Wald, exact, Agresti-Coull, and likelihood intervals. While the Wilson interval may not be the most conservative estimate, it produces
Coverage probability
466294
the regional variant) at the end of syllables. In Basque, it represents the sound . In Danish, Norwegian, and Swedish, usually stands for the sound /s/ and thus shares the value of ; it normally occurs only in loanwords that are spelt with in the source languages. The letter on its own represents in Polish. It is also used in four of the seven officially recognized digraphs: (), ( or ), ( or , sometimes it represents a sequence ) and (), and is the most frequently used of the consonants in that language. (Other Slavic languages avoid digraphs and
Z
223152
differ. In this case, the Kolmogorov–Smirnov statistic is where formula_38 and formula_39 are the empirical distribution functions of the first and the second sample respectively, and formula_40 is the supremum function. The null hypothesis is rejected at level formula_25 if Where formula_5 and formula_44 are the sizes of first and second sample respectively. The value of formula_45 is given in the table below for the most common levels of formula_25 and in general by Note that the two-sample test checks whether the two data samples come from the same distribution. This does not specify what that common distribution is (e.g.
Kolmogorov–Smirnov test
8705954
on the western border of the Pantanal. It is a terrestrial species. A study of small rodents in Peru found that "E. nitidus" is the fourth most frequently caught species, with 35 individuals trapped out of a total of 362 rodents; six of this total harboured a hantavirus variant, IgG, including an adult male "E. nitidus". Hantaviruses can cause hantavirus pulmonary syndrome in the human population, and although the occurrence of this syndrome is currently low, when it occurs, this zoonotic disease is often fatal. "E. nitidus" is a common species with a wide distribution. It is present in a
Euryoryzomys nitidus
993769
using the following equation: The resulting UCL will be the greatest average value that will occur for a given confidence interval and population size. In other words, formula_96 being the mean of the set of observations, the probability that the mean of the distribution is inferior to UCL is equal to the confidence level 1 − "α". The "t"-distribution can be used to construct a prediction interval for an unobserved sample from a normal distribution with unknown mean and variance. The Student's "t"-distribution, especially in its three-parameter (location-scale) version, arises frequently in Bayesian statistics as a result of its connection
Student's t-distribution
3544124
for B in the column above the cell occurs, as 2/3. Thus the marginal probability distribution for A gives A's probabilities "unconditional" on B, in a margin of the table. Consider the flip of two fair coins; let "A" and "B" be discrete random variables associated with the outcomes of the first and second coin flips respectively. Each coin flip is a Bernoulli trial and has a Bernoulli distribution. If a coin displays "heads" then the associated random variable takes the value 1, and it takes the value 0 otherwise. The probability of each of these outcomes is 1/2, so
Joint probability distribution
8346500
the NULL value. NULL is frequently used to represent a missing value or invalid value, such as from a function that failed to return or a missing field in a database, as in NULL in SQL. An integer variable may represent integers, but 0 (zero) is a special case because 0 in many programming languages can mean "false". Also this doesn't give us any notion of saying that the variable is empty, a need for which occurs in many circumstances. This need can be achieved with a nullable type. In programming languages like C# 2.0, a nullable integer, for example,
Nullable type
9440754
"P. dominula" is often referred to as the European paper wasp because of its native distribution and its nests, which are constructed from paper and saliva. It is also frequently referred to in older literature as "Polistes gallicus", a separate species with which it was often confused. Little variation occurs among individuals of "P. dominula"; the wing lengths of males range from 9.5 to 13.0 mm, while those of females range from 8.5 to 12.0 mm. Its body is colored entirely yellow and black, similar to that of "Vespula germanica", one of the most common and aggressive wasps in its
Polistes dominula
14241119
Substitution (algebra) In algebra, the operation of substitution can be applied in various contexts involving formal objects containing symbols (often called variables or indeterminates); the operation consists of systematically replacing occurrences of some symbol by a given value. Substitution is a basic operation of computer algebra. It is generally called "subs" or "subst" in computer algebra systems. A common case of substitution involves polynomials, where substitution of a numerical value for the indeterminate of a (univariate) polynomial amounts to evaluating the polynomial at that value. Indeed this operation occurs so frequently that the notation for polynomials is often adapted to
Substitution (algebra)
18232304
min-entropy; this means that its statistical distance from a string with formula_16 min-entropy is no larger than formula_15. Reminder: There are several notions of measuring the randomness of a distribution; the min-entropy of a random variable formula_19 is defined as the largest formula_1 such that the most probable value of formula_19 occurs with probability no more than formula_22. The min-entropy of a string is an upper bound to the amount of randomness that can be extracted from it. There are three parameters to optimize when building mergers: Explicit constructions for mergers are known with relatively good parameters. For example, Dvir
Randomness merger
15999737
Himalayan mountain chain. It has been suggested that the genus may have originated in this area and then spread westwards along the Himalayas and eastwards into the mountains of China and its southern neighbours. "R. tumjensis" falls into the Himalayan clade as would be expected from its distribution. "Roscoea tumjensis" occurs in the Himalayas, in central and eastern Nepal. The type specimen was collected at an altitude of 2,740 m. "R. tumjensis" is in cultivation in the UK, frequently incorrectly labelled "R. brandisii". Roscoea tumjensis Roscoea tumjensis is a perennial herbaceous plant occurring in the Himalayas, in Nepal. Most members
Roscoea tumjensis
11059773
methods of control currently include spraying more frequently with higher surveillance or to devise a strategy that attacks "T. brasiliensis" in sylvatic foci such as spraying palm trees. Triatoma brasiliensis Triatoma brasiliensis Neiva, 1911 is now considered the most important Chagas disease vector in the semiarid areas of northeastern Brazil. "T. brasiliensis" occurs in 12 Brazilian states, including Maranhão, Piauí, Ceará, Rio Grande do Norte, and Paraíba. "T. brasiliensis" is native to this part of Brazil, and thus persists in the natural environment. This species of Kissing Bug has the greatest potential to spread Chaga's disease due to its distribution
Triatoma brasiliensis
10649905
the eye and white behind. The upper parts are dark, brownish-black, the flanks are dusky grey and the underparts magenta, as is the leading edge of the wing. The female is generally similar to the male but the rosy-magenta is replaced by a deep ochre colour. The beak is long and slightly curved, resembling that of a mimid. The distribution in Central America and northern South America includes Mexico, Costa Rica, northern Venezuela and northern Colombia. Typical habitat is thick undergrowth in deciduous forests, secondary woodland, thickets and scrubland. It most frequently occurs in the mountain foothills at altitudes varying
Rosy thrush-tanager
2669855
the amount of distortion of a pixel value against the frequency with which it occurs, shows a normal distribution of noise. While other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to the central limit theorem that says that the sum of different noises tends to approach a Gaussian distribution. In either case, the noise at different pixels can be either correlated or uncorrelated; in many cases, noise values at different pixels are modeled as being independent and identically distributed, and hence uncorrelated. In selecting a noise reduction algorithm, one must weigh several factors: In
Noise reduction
367831
brother Frithiof, extended the theory to cover meromorphic functions, i.e. functions analytic in the plane except for isolated points in which the Laurent series of the function has a finite number of terms with a negative power of the variable. Nevanlinna's value distribution theory or Nevanlinna theory is crystallised in its two "Main Theorems". Qualitatively, the first one states that if a value is assumed less frequently than average, then the function comes close to that value more often than average. The Second Main Theorem, more difficult than the first one, states roughly that there are relatively few values which
Rolf Nevanlinna
559270
there are failures in total. So we would expect , so . See that is just the average number of trials per experiment. That is what we mean by "expectation". The average number of successes per experiment is , which must have expected value equal to . This agrees with the mean given in the box on the right-hand side of this page. When counting the number "k" of successes given the number "r" of failures, the variance is "r(1-p)"/("p"). Some sources may define the negative binomial distribution slightly differently from the primary one here. The most common variations are
Negative binomial distribution
20252234
distribution assigns very small probability to extreme values, particularly to the extreme furthest away from the most likely value if the distribution is strongly skewed . The Modified PERT distribution was proposed to provide more control on how much probability is assigned to tail values of the distribution. The modified-PERT introduces a fourth parameter formula_12 that controls the weight of the most likely value in the determination of the mean: Typically, values of between 2 and 3.5 are used for formula_12 and have the effect of flattening the density curve. This is useful for highly-skewed distributions where the distances formula_15
PERT distribution
7343084
tail is more ambiguous, because in this parameter range, the variance, skewness, and kurtosis can be finite, depending on the precise value of formula_4, and thus potentially smaller than a high-variance normal or exponential tail. This ambiguity often leads to disagreements about precisely what is or is not a fat-tailed distribution. Note: here the tilde notation "formula_6" refers to the asymptotic equivalence of functions, meaning that there exists some finite value of formula_7 above which the probability distribution follows the right-hand side of the expression. In other words, asymptotically, the tail of the distribution decays like a power law. Compared
Fat-tailed distribution
16171718
thin geometric profile of the disk allows for an uneven distribution of mass with an inertial axis that is nearly parallel to the axis of rotation. Only one plane receives balance correction. where U = balance, m = mass, r = distance between unbalance and the centre of the object A couple balance occurs when a rotating mass has two equal unbalance forces that are situated 180° opposite each other. A system that is statically balanced may still have a couple unbalance. Couple unbalance occurs frequently in elongated cylindrical rotors. where d = distance between the two unbalance forces along
Rotating unbalance
364093
risks to a male's fitness, such as high energy expenditure, physical injury, lower sperm quality and lost paternity. The risk of competition must therefore be worth the value of the resource. A male is more likely to engage in competition for a resource that improves their reproductive success if the resource value is higher. While male-male competition can occur in the presence or absence of a female, competition occurs more frequently in the presence of a female. The presence of a female directly increases the resource value of a territory or shelter and so the males are more likely to
Sexual selection
10329296
Value-action gap The value-action gap is the space that occurs when the values (personal and cultural) or attitudes of an individual do not correlate to his or her actions. More generally, it is the difference between what people say and what people do. The phrase is associated with environmental geography, relating to attitudes and behaviors surrounding environmental issues. Usually attitudes affect behavior; however the opposite often seems to be the case with regard to environmental attitudes and values. The outcome is that there is a gap between the high value people place on the natural environment and the relatively low
Value-action gap
7521322
than from scan to scan. Examples include some helicopters and propeller driven aircraft. Constant RCS, corresponding to infinite degrees of freedom (formula_13). Chi-squared target models Swerling models were introduced by Peter Swerling and are used to describe the statistical properties of the radar cross-section of complex objects. Swerling target models give the radar cross-section (RCS) of a given object using a distribution in the location-scale family of the chi-squared distribution. where formula_2 refers to the mean value of formula_3. This is not always easy to determine, as certain objects may be viewed the most frequently from a limited range of
Chi-squared target models
2510408
distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set. Using the ideas of Kolmogorov complexity, one can consider the mutual information of
Mutual information
13395411
world ("verkehrte Welt") of trading processes, and he adds satirically in a footnote that “in a certain sense, people are in the same situation as commodities…”. The suggestion is that, by analogy, the recognition of a person's identity and worth occurs only through contact with other people, and that one person becomes the species-model for another, just as commodities need to relate to each other and to money to establish what the magnitude of their value is. Marx's description of what goes on in commodity exchanges highlights not only that value relationships appear to exist between commodities quite independently of
Value-form
11087815
"ν" degrees of freedom. In applications, the "x" are typically the means of samples each of size "m", "s" is the pooled variance, and the degrees of freedom are "ν" = "n"("m" − 1). The critical value of "q" is based on three factors: If "X", ..., "X" are independent identically distributed random variables that are normally distributed, the probability distribution of their studentized range is what is usually called the studentized range distribution. Note that the definition of "q" does not depend on the expected value or the standard deviation of the distribution from which the sample is drawn,
Studentized range
302580
that this distribution was seen as typical, common – and thus "normal". Peirce (one of those authors) once defined "normal" thus: "...the 'normal' is not the average (or any other kind of mean) of what actually occurs, but of what "would", in the long run, occur under certain circumstances." Around the turn of the 20th century Pearson popularized the term "normal" as a designation for this distribution. Also, it was Pearson who first wrote the distribution in terms of the standard deviation "σ" as in modern notation. Soon after this, in year 1915, Fisher added the location parameter to the
Normal distribution
204673
the entropy (in bits) is equal to this number. If one of the values is more probable to occur than the others, an observation that this value occurs is less informative than if some less common outcome had occurred. Conversely, rarer events provide more information when observed. Since observation of less probable events occurs more rarely, the net effect is that the entropy (thought of as average information) received from non-uniformly distributed data is always less than or equal to . Entropy is zero when one outcome is certain to occur. The entropy quantifies these considerations when a probability distribution
Entropy (information theory)
11592744
of a specific output value must be considered when determining what is an acceptable M/U ratio for that performance variable. If the uncertainty limit for U includes a finite upper bound due to the particular distribution of that variable, a lower M/U ratio may be acceptable. However, if U is modeled as a normal or exponential distribution which can potentially include outliers from the far tails of the distribution, a larger value may be required in order to reduce system risk to an acceptable level. Ratios of acceptable M/U for safety critical systems can vary from application to application. Studies
Quantification of margins and uncertainties
11374319
emphasizes that the penalty is exercised only when ruin occurs. It is quite intuitive to interpret the expected discounted penalty function. Since the function measures the actuarial present value of the penalty that occurs at formula_28, the penalty function is multiplied by the discounting factor formula_29, and then averaged over the probability distribution of the waiting time to formula_28. While Gerber and Shiu applied this function to the classical compound-Poisson model, Powers argued that an insurer’s surplus is better modeled by a family of diffusion processes. There are a great variety of ruin-related quantities that fall into the category of
Ruin theory
3803810
Over-investing Over-investing in finance, particularly personal finance, refers to the practice of investing more into an asset than what that asset is worth on the open market. It is cited most frequently in reference to expensive personal consumable investments such as houses, automobiles, and trailers. If a homeowner makes additions or improvements to her house to the point that the owner has invested considerably more than the market value of other houses in that area, then she has likely over-invested in that house. The "neighbourhood effect" will serve to devalue the house so that it is worth less than what
Over-investing
13474891
the economic crisis, and the value of an insight in the workplace. Zaltman metaphor elicitation technique The Zaltman metaphor elicitation technique (ZMET) is a market research tool. ZMET is a technique that elicits both conscious and especially unconscious thoughts by exploring people's non-literal or metaphoric expressions. It was developed by Dr. Gerald Zaltman at the Harvard Business School in the early 1990s. As Zaltman described it, "A lot goes on in our minds that we're not aware of. Most of what influences what we say and do occurs below the level of awareness. That's why we need new techniques: to
Zaltman metaphor elicitation technique
1319329
left bound on the outcome. A casino doesn't worry about whether red or black will come up on the next roulette spin. Risk managers encourage productive risk-taking in this regime, because there is little true cost. People tend to worry too much about these risks, because they happen frequently, and not enough about what might happen on the worst days. Outside the VaR limit, all bets are off. Risk should be analyzed with stress testing based on long-term and broad market data. Probability statements are no longer meaningful. Knowing the distribution of losses beyond the VaR point is both impossible
Value at risk
16466240
can lose significantly more than the price they paid to buy the product.) The probability of ruin is approximately where for a random walk with a starting value of "s", and at every iterative step, is moved by a normal distribution having mean "μ" and standard deviation "σ" and failure occurs if it reaches 0 or a negative value. For example, with a starting value of 10, at each iteration, a Gaussian random variable having mean 0.1 and standard deviation 1 is added to the value from the previous iteration. In this formula, "s" is 10, "σ" is 1, "μ"
Risk of ruin
16025226
µ, and the standard deviation, σ, of Fi. However, choosing Morris has the drawback that, if the distribution, Fi , contains negative elements, which occurs when the model is non-monotonic, when computing the mean some effects may cancel each other out. Thus, the measure µ on its own is not reliable for ranking factors in order of importance. It is necessary to consider at the same time the values of µ and σ, as a factor with elementary effects of different signs (that cancel each other out) would have a low value of µ but a considerable value of σ
Morris method
9888464
the third (middle) piece has several terms, generically middle, also belly, torso, and body. These frequently have some adjectives added, most significantly "long tail", also "fat belly", "chunky middle", etc. In more traditional terms, these may be called "top-tier", "mid-tier", and "bottom-tier". The relative sizes and weights of these segments (how many ranks in each segment, and what proportion of the total population is in a given segment) qualitatively characterizes a distribution, analogously to the skewness or kurtosis of a probability distribution. Namely: is it dominated by a few top members (head-heavy, like profits in the recorded music industry), or
Rank-size distribution
3880127
and distribution channel management. Yield management is multidisciplinary because it blends elements of marketing, operations, and financial management into a highly successful new approach. Yield management strategists must frequently work with one or more other departments when designing and implementing yield management strategies. Deregulation is generally regarded as the catalyst for yield management in the airline industry, but this tends to overlook the role of Global Distribution Systems (GDSs). It is arguable that the fixed pricing paradigm occurs as a result of decentralized consumption. With mass production, pricing became a centralized management activity and customer contact staff focused on customer
Yield management
11355154
term in many regressions. That the result based on 'r-1' is wrong is readily seen by considering r = 2, as in a standard simple linear regression. That formula would then reduce to one with the usual t distribution, which is appropriate for predicting/estimating for a single value of the independent variable, not for constructing a confidence band for a range of values of the independent value. Also note that the formula is for dealing with the mean values for a range of independent values, not for comparing with individual values such as individual observed data values. Frequently, superscript letters
Scheffé's method
1858260
that lie in it, up to some integer "N", and compare it to the proportion of the circumference occupied by "I". "Uniform distribution" means that in the limit, as "N" grows, the proportion of hits on the interval tends to the 'expected' value. Hermann Weyl proved a basic result showing that this was equivalent to bounds for exponential sums formed from the sequence. This showed that Diophantine approximation results were closely related to the general problem of cancellation in exponential sums, which occurs throughout analytic number theory in the bounding of error terms. Related to uniform distribution is the topic
Diophantine approximation
1660493
= 1.49835 approaches the upper limit of 1.5 from below. An example of a beta distribution near the lower boundary (excess kurtosis + 2 − skewness = 0) is given by α= 0.0001, β = 0.1, for which values the expression (excess kurtosis + 2)/(skewness) = 1.01621 approaches the lower limit of 1 from above. In the infinitesimal limit for both α and β approaching zero symmetrically, the excess kurtosis reaches its minimum value at −2. This minimum value occurs at the point at which the lower boundary line intersects the vertical axis (ordinate). (However, in Pearson's original chart, the
Beta distribution
126272
product of the lengths is then either The stated result follows because the maximum value of formula_8 occurs at formula_9 (Steiner's problem, discussed below). The quantity formula_8 is a measure of information gleaned from an event occurring with probability formula_11, so that essentially the same optimal division appears in optimal planning problems like the secretary problem. The number occurs naturally in connection with many problems involving asymptotics. An example is Stirling's formula for the asymptotics of the factorial function, in which both the numbers and enter: As a consequence, The normal distribution with zero mean and unit standard deviation is
E (mathematical constant)
9808010
generally used, including most prominently contingent valuation methods (CVM). Non-use value Non-use value is the value that people assign to economic goods (including public goods) even if they never have and never will use it. It is distinguished from use value, which people derive from direct use of the good. The concept is most commonly applied to the value of natural and built resources. Non-use value as a category may include: Rick Freeman (1993) suggests yet another variant that he calls "pure non-use value", defined as the value that occurs for an individual when current prices preclude use of a
Non-use value
10289615
its own bucket. This ensures that the estimate for that value (which is likely to be the most frequently requested estimate, since it is the most frequent value) will always be accurate and also removes the value most likely to cause a high variance from the data set. Another thought that might occur is that variance would be reduced if one were to sort by frequency, instead of value. This would naturally tend to place like values next to each other. Such a histogram can be constructed by using a Sort Value of Frequency and a Source Value of Frequency.
V-optimal histograms
392023
animals that are not their usual hosts, but such infections do not last long. Scabies-infected animals suffer severe itching and secondary skin infections. They often lose weight and become frail. The most frequently diagnosed form of scabies in domestic animals is sarcoptic mange, caused by the subspecies "Sarcoptes scabiei canis", most commonly in dogs and cats. Sarcoptic mange is transmissible to humans who come into prolonged contact with infested animals, and is distinguished from human scabies by its distribution on skin surfaces covered by clothing. Scabies-infected domestic fowl suffer what is known as "scaly leg". Domestic animals that have gone
Scabies
2081750
major thirds is from 396 cents to 404 cents, or ten cents sharp of just 5/4 to three cents flat of Pythagorean 81/64. These intervals fall within what is considered to have been acceptable but there is no distribution of better thirds to more frequently used keys that characterize what are today the most popular of the tunings published in the seventeenth and eighteenth centuries, which are known as "well temperaments". The best fifth is pure in the key of F♯—or the pitch given by "MB"—which has a 398 cent third, and the best third is in the key E,
Strähle construction
6981059
generally respond better to treatment but have shorter survival times than dogs with low grade lymphoma. Dogs with B-lymphocyte tumors have a longer survival time than T-lymphocyte tumors. Mediastinal lymphoma has a poorer prognosis than other types, especially those with hypercalcemia. Clinical stage and substage have some prognostic value, with poorer prognosis associated with Stage V disease, and with substage b (clinical illness at time of presentation). Lymphoma is the most common malignancy diagnosed in cats. Lymphoma in young cats occurs most frequently following infection with feline leukemia virus (FeLV) or to a lesser degree feline immunodeficiency virus (FIV). These
Lymphoma in animals
13678181
and main habitat, the white spruce. The moth, transcontinental in range, is found most frequently on white spruce and only occasionally on other spruces and firs. The larvae of the spruce bud moth hatch in the buds of white spruce trees. Much of its development, adult life, ovipositing and mating occurs on this tree, making it a key aspect of the moth’s life cycle and habitat. Consequently, the distribution of the moth is limited to regions with high density of white spruce trees, such as Canada and other Northern temperate regions. Female spruce bud moths oviposit on the un-burst buds
Zeiraphera canadensis
14760144
sign that is needed when the variable occurs in the lower limit of the integration.) formula_12 where the absolute value is used to conveniently combine the two terms. A faster more compact proof begins with the same step of writing the cumulative distribution of formula_8 starting with its definition: formula_14 where formula_15 is the Heaviside step function and serves to limit the region of integration to values of formula_16 and formula_17 satisfying formula_18. We find the desired probability density function by taking the derivative of both sides with respect to formula_10. formula_20 where we utilize the translation and scaling properties
Product distribution
6668442
are presumed to be negligible. For example, the Wagner effect says that circulation rises slowly to its steady-state due to viscosity when an inclined wing is accelerated from rest. This phenomenon would explain a lift value that is less than what is predicted. Typically, the case has been to find sources for the added lift. It has been argued that this effect is negligible for flow with a Reynolds number that is typical of insect flight. The Wagner effect was ignored, consciously, in at least one recent model. One of the most important phenomena that occurs during insect flight is
Insect flight
19476924
notion of manipulating a psychology around stimulus and response found in Aristotilian or Cartesian thought. A transaction is recognized here as one that occurs between the "means and ends;" in other words, transactional competence is derived from the "distinctions between the how, the what (or subject-matter), and the why (or what for)." This transactional whole constitutes a reciprocal connection and a reflexive arc of learned and lived experience. From a transactional approach one can derive a certain kind of value from one's social exchange. Value in knowing how, what, and why the work done with your mind and body fulfill
Transactionalism
7433440
Social discount rate Social discount rate (SDR) is the discount rate used in computing the value of funds spent on social projects. Determining this rate is not always easy and can be the subject of discrepancies in the true net benefit to certain projects, plans and policies. The discount rate is considered as a critical element in cost-benefit analysis when the costs and the benefits differ in their distribution over time, this usually occurs when the project that is being studied is over a long period of time. It may be used in estimating the value of creating a highway
Social discount rate
3258186
occur frequently, though Irish law never strictly defines them. Similarly, the term "córus" (law in accordance with proper order) occurs in some places, and even in the titles of certain texts. The laws tell stories of how truth could apparently cure a person and falsehood could cause blisters. These were two very real concepts to the jurists and the value of a given judgment with respect to them was apparently ascertainable. McLeod has also suggested that most of the specific laws mentioned have passed the test of time and thus their truth has been confirmed, while other provisions are justified
Early Irish law
7965681
probably been studied the most and it is therefore relatively well understood. Many linguists take pseudogapping to be a particular manifestation of VP-ellipsis (not of gapping). Like VP-ellipsis, pseudogapping is introduced by an auxiliary verb. Pseudogapping differs from VP-ellipsis, however, insofar as the elided VP is not entirely gone, but rather one (or more) remnants of the VP appear. This aspect of pseudogapping gives it the outward appearance of gapping. Pseudogapping occurs frequently in comparative and contrastive contexts: Pseudogapping is more restricted in distribution than VP-ellipsis. For instance it can hardly occur backwards, i.e. the ellipsis can hardly precede its
Ellipsis (linguistics)
15469495
Corporate and Industrial Change, edited by Mazzucato, describes the tension between how value is created and how value is extracted in modern-day capitalism. The authors argue that there is a disproportionate balance between the 'collective' distribution of risk taking in the innovation process, and the increasingly narrow distribution of the rewards. The paper was first published in a 2012 paper for the think tank Policy Network. Similarly, in another paper for the think tank Policy Network called "Rebalancing What?", Mazzucato argues that the problem is not only one of short-termism, it is also about the way in which financial activities
Mariana Mazzucato
239591
logarithm of a random variable has a normal distribution, the variable is said to have a log-normal distribution. Log-normal distributions are encountered in many fields, wherever a variable is formed as the product of many independent positive random variables, for example in the study of turbulence. Logarithms are used for maximum-likelihood estimation of parametric statistical models. For such a model, the likelihood function depends on at least one parameter that must be estimated. A maximum of the likelihood function occurs at the same parameter-value as a maximum of the logarithm of the likelihood (the ""log likelihood""), because the logarithm is
Logarithm
20252235
and formula_16 are of very different sizes. The modified-PERT distribution has been implemented in several simulation packages: PERT distribution where formula_1 formula_2 (the incomplete beta function) with formula_4 In probability and statistics, the PERT distribution is a family of continuous probability distributions defined by the minimum (a), most likely (b) and maximum (c) values that a variable can take. It is a transformation of the four-parameter Beta distribution with an additional assumption that its expected value is The mean of the distribution is therefore defined as the weighted average of the minimum, most likely and maximum values that the variable
PERT distribution
13017019
the income affects the utility linearly, then If the researcher believes that the sociodemographic variable interacts with other variable such as price, then the utility can be written as As mentioned earlier, calculation and justification of choice probabilities rely on the properties of the error (i.e. the unobservables) distribution function the researcher specifies. Here is the quick overview of frequently used models that each differs in specification 1. Logit: 2. GEV (Generalized extreme value distribution) 3. Probit 4. Mixed logit Choice model simulation Although the concept choice models is widely understood and practiced these days, it is often difficult to
Choice model simulation
11937125
only occasionally in winter, with temperatures below -10 °C being very uncommon in the lowlands, and temperatures below freezing uncommon in many coastal areas, although temperatures in the Wicklow Mountains are said to reach -10 °C annually. Air frost occurs frequently in the winter, with most areas seeing over 40 days of air frost every year. In northern areas, air frost occurs on average 10.2 days every January, the month in which air frost occurs most frequently. In the Sperrins and the Glens of Antrim air frost occurs around 80 days a year. The pattern is similar with ground frost,
Climate of Ireland
6553403
"Y" is dichotomous. We could calculate the coefficient in the same way as where "X" is continuous but it would have the same disadvantage that the range of values it can take on becomes more constrained as the distribution of "Y" becomes more unequal. To get round this, we note that the coefficient will have its largest value where the smallest ranks are all opposite the 0s and the largest ranks are opposite the 1s. Its smallest value occurs where the reverse is the case. These values are respectively plus and minus ("n" + "n")/2. We can therefore use the
Point-biserial correlation coefficient
15456652
consistently a statistically significant relationship was identified across multiple studies. The authors claim that the review summarizes most of what is currently known about the variables associated with criminality. Crime occurs most frequently during the second and third decades of life. Males commit more crime overall and more violent crime than females. They commit more property crime except shoplifting, which is about equally distributed between the genders. Males appear to be more likely to reoffend. Measures related to arousal such as heart rate and skin conductance are low among criminals. Mesomorphic or muscular body type is positively correlated with criminality,
Statistical correlations of criminal behaviour
16368
just integers, then the probability of a number falling into some range of possible values can be described by integrating a continuous probability distribution across this range, even when the naive probability for a sample number taking one certain value from infinitely many is zero. The analog of a weighted average in this context, in which there are an infinite number of possibilities for the precise value of the variable in each range, is called the "mean of the probability distribution". A most widely encountered probability distribution is called the normal distribution; it has the property that all measures of
Arithmetic mean
18135612
binomial distribution, where the "probability of success" is "p" and the sample size is "n": we can show that the median test derived with th IDP for any choice of formula_95 encompasses the one-sided frequentist sign test as a test for the median. It can in fact be verified that for formula_96 the formula_97-value of the sign test is equal to formula_98. Thus, if formula_99 then the formula_97-value is less than formula_101 and, thus, they two tests have the same power. Dirichlet processes are frequently used in Bayesian nonparametric statistics. The Imprecise Dirichlet Process can be employed instead of the
Imprecise Dirichlet process
10285344
and dividing it by the number of samples. Simulations have shown this distribution to be conservative, and now that the computing power is more readily available this approximation is not frequently used. A more nuanced approach was presented in a paper by Simonsen et al. These authors advocated constructing a confidence interval for the true theta value, and then performing a grid search over this interval to obtain the critical values at which the statistic is significant below a particular alpha value. An alternative approach is for the investigator to perform the grid search over the values of theta which
Tajima's D
1620471
possess different bargaining power (for example threatening to destroy the whole surplus), what final distribution of generated surplus among the players should arise in any particular game? Or phrased differently: how important is each player to the overall cooperation, and what payoff can he or she reasonably expect? The Shapley value provides one possible answer to this question. For cost-sharing games with concave cost functions, the optimal cost-sharing rule that optimizes the price of anarchy, followed by the price of stability, is precisely the Shapley value cost-sharing rule. Formally, a coalitional game is defined as: There is a set "N"
Shapley value