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

(1)

for
where
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
See also
Pearson Type IV Distribution
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References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, 1972.Referenced on WolframAlpha
Pearson Type III Distribution
Cite this as:
Weisstein, Eric W. "Pearson Type III Distribution."
From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/PearsonTypeIIIDistribution.html
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