(Symbol β2 or α4. ) A descriptive measure of a random variable in terms of the flatness of its probability distribution. It is defined as follows:

where μ4 is the fourth (statistical) moment about the mean and σ2 the variance. For the normal distribution, β2 = 3; and it is commonly (though not invariably) found that curves for which β2 > 3 are more sharply peaked than the normal, while those for which β2 < 3 are flatter than the normal. In particular, the rectangular distribution f(x) = 1 (0 < x < 1) has β2 = 1. 8. The terms leptokurtic, mesokurtic, and platykurtic refer to curves for which the values of β2 are, respectively, greater than 3, equal to 3, and less than 3. Excess is a relative expression for kurtosis, and the coefficient of excess γ2 is defined as β2 − 3.