The distribution with probability density function and distribution function

			(1)
			(2)

defined over the interval .

It is implemented in Mathematica as ParetoDistribution[k, alpha].

The th raw moment is

(3)

for , giving the first few as

			(4)
			(5)
			(6)
			(7)

The th central moment is

			(8)
			(9)
			(10)
			(11)

for and where is a gamma function, is a regularized hypergeometric function, and is a beta function, giving the first few as

			(12)
			(13)
			(14)

The mean, variance, skewness, and kurtosis are therefore

			(15)
			(16)
			(17)
			(18)

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 252, 1993.

CITE THIS AS:

Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ParetoDistribution.html