In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion − ln ( 1 − p ) = p + p 2 2 + p 3 3 + ⋯ . {\displaystyle -\ln(1-p)=p+{\frac {p^{2}}{2}}+{\frac {p^{3}}{3}}+\cdots .} From this we obtain the identity ∑ k = 1 ∞ − 1 ln ( 1 − p ) p k k = 1.
In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion − ln ( 1 − p ) = p + p 2 2 + p 3 3 + ⋯ . {\displaystyle -\ln(1-p)=p+{\frac {p^{2}}{2}}+{\frac {p^{3}}{3}}+\cdots .} From this we obtain the identity ∑ k = 1 ∞ − 1 ln ( 1 − p ) p k k = 1.
Source: Wikipedia "Logarithmic distribution" · CC BY-SA 4.0
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