Log-Series Distribution

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of the terms in the series expansion of about . It has probability and density functions given by

			(1)
			(2)

where is the incomplete beta function.

The log-series distribution is implemented as LogSeriesDistribution[theta].

It is properly normalized since

(3)

The th raw moment is given by

(4)

where is a polylogarithm.

The mean, variance, skewness, and kurtosis excess

			(5)
			(6)
			(7)
			(8)