Pearson (not to be confused with Pearson's moment coefficient of skewness, see above). These other measures are: Pearson's first skewness coefficient (mode skewness) The Pearson mode skewness, or first skewness coefficient, is defined as . Pearson's second skewness coefficient (median skewness) The Pearson median skewness, or second skewness coefficient, is defined as . Which is a simple multiple of the nonparametric skew. Quantile-based measures Bowley's measure of skewness (from 1901), also called Yule's coefficient (from 1912) is defined as: where Q is the quantile function (i.e., the inverse of the cumulative distribution function). The numerator is difference between the average of the upper and lower quartiles (a measure of location) and the median (another measure of location), while the denominator is the semi-interquartile range , which for symmetric distributions is the MAD measure of dispersion. Other names for this measure are Galton's measure of skewness, the Yule–Kendall index and the quartile skewness, Similarly, Kelly's measure of skewness is defined as A more general formulation of a skewness function was described by Groeneveld, R. A. and Meeden, G. (1984):<ref name=Hinkley1975>Hinkley DV (1975) "On power transformations to symmetry", Biometrika, 62, 101–111</ref> The function γ(u) satisfies −1 ≤ γ(u) ≤ 1 and is well defined without requiring the existence of any moments of the distribution. Bowley's measure of skewness is γ(u) evaluated at u = 3/4 while Kelly's measure of skewness is γ(u) evaluated at u = 9/10. This definition leads to a corresponding overall measure of skewness defined as the supremum of this over the range 1/2 ≤ u < 1. Another measure can be obtained by integrating the numerator and denominator of this expression. Quantile-based skewness measures are at first glance easy to interpret, but they often show significantly larger sample variations than moment-based methods. This means that often samples from a symmetric distribution (like the uniform distribution) have a large quantile-based skewness, just by chance. Groeneveld and Meeden's coefficient Groeneveld and Meeden have suggested, as an alternative measure of skewness, where μ is the mean, ν is the median, |...| is the absolute value, and E() is the expectation operator. This is closely related in form to Pearson's second skewness coefficient. L-moments Use of L-moments in place of moments provides a measure of skewness known as the L-skewness. Distance skewness A value of skewness equal to zero does not imply that the probability distribution is symmetric. Thus there is a