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 
.
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Distribution name
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Logarithmic
distribution
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Common notation
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Parameters
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 =
shape parameter ( )
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Domain
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Probability mass
function
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Cumulative distribution
function
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Mean
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Variance
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Skewness
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(Excess) kurtosis
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where
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Characteristic function
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Other comments
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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
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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.
NAVIGATION LINKS
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