Pearson Type III Distribution

A skewed distribution which is similar to the binomial distribution when  (Abramowitz and Stegun 1972, p. 930).

(1)

for  where

			(2)
			(3)

 is the gamma function, and  is a standardized variate. Another form is

(4)

For this distribution, the characteristic function is

(5)

and the mean, variance, skewness, and kurtosis excess are

			(6)
			(7)
			(8)
			(9)

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.