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Date: 11-2-2021
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Date: 19-2-2021
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Date: 24-2-2021
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The logarithmic distribution is a continuous distribution for a variate with probability function
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(1) |
and distribution function
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(2) |
It therefore applies to a variable distributed as , and has appropriate normalization.
Note that the log-series distribution is sometimes also known as the logarithmic distribution, and the distribution arising in Benford's law is also "a" logarithmic distribution.
The raw moments are given by
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(3) |
The mean is therefore
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(4) |
The variance, skewness, and kurtosis excess are slightly complicated expressions.
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