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# A to Z of Excel Functions: the BETAINV Function

9 December 2016

Welcome back to our regular A to Z of Excel Functions blog.  Today we look at the BETAINV function.

The BETAINV function

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrised by two positive shape parameters, denoted by α (alpha) and β (beta), that appear as exponents of the random variable and control the shape of the distribution.  It has nothing to do with either the beta function (Euler integral) used in other areas of mathematics or the beta cited as the scalar in the Capital Asset Pricing Model.

The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines.  For example, it has been used as a statistical description of allele frequencies in population genetics, time allocation in project management / control systems, sunshine data, variability of soil properties, proportions of the minerals in rocks in stratigraphy and heterogeneity in the probability of HIV transmission.  Who’d have thought statistics and Excel could be so interesting?

In Bayesian inference, the beta distribution is the conjugate prior probability distribution for the Bernoulli, binomial, negative binomial and geometric distributions.  For example, the beta distribution can be used in Bayesian analysis to describe initial knowledge concerning probability of success such as the probability that a space vehicle will successfully complete a specified mission.  The beta distribution is a suitable model for the random behavior of percentages and proportions.

The usual formulation of the beta distribution is also known as the beta distribution of the first kind, whereas beta distribution of the second kind is an alternative name for the beta prime distribution.

The BETAINV function returns the inverse of the cumulative beta probability density function for a specified beta distribution. That is, if probability = BETADIST(x,...), then BETAINV(probability,...) = x. The beta distribution can be used in project planning to model probable completion times given an expected completion time and variability.

It should be noted that this function has been replaced with one or more new functions from Excel 2010 onwards (BETA.INV) that may provide improved accuracy and whose names better reflect their usage.  Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

The BETAINV function employs the following syntax to operate:

BETAINV(x,alpha,beta,cumulative,[A],[B])

The BETAINV function has the following arguments:

• probability: required.  This represents a probability associated with the beta distribution
• alpha: also required.  This is a parameter of the distribution
• beta: required.  This is also a parameter the distribution
• A: optional.  This is a lower bound to the interval of x
• B: this is also optional.  This is an upper bound to the interval of x.

It should be further noted that:

• If any argument is nonnumeric, BETAINV returns the #VALUE! error value
• If alpha ≤ 0 or beta ≤ 0, BETAINV returns the #NUM! error value
• If probability ≤ 0 or probability > 1, BETAINV returns the #NUM! error value
• If you omit values for A and B, BETAINV uses the standard cumulative beta distribution, so that A = 0 and B = 1.
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