The logarithmic distribution
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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.
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