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### The logarithmic distribution

The logarithmic distribution arises from following power series expansion: This means that the function , can naturally be interpreted as a probability mass function since .

 Distribution name Logarithmic distribution Common notation Parameters = shape parameter ( ) Domain Probability mass function Cumulative distribution function Mean Variance Skewness (Excess) kurtosis where Characteristic function Other comments The logarithmic distribution has a mode  of 1. If is a random variable with Poission distribution and , is an infinite sequence of iid random variables each distributed then has a negative binomial distribution showing that the negative binomial distribution is an example of a compound Poisson distribution

Nematrian web functions

Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “logarithmic”. For details of other supported probability distributions see here.