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·       Format:

Logarithmic (θ)

·       Probability mass function:

f(x)= \frac {-\theta^x}{xln (1- \theta)}

·       Cumulative distribution function:

F(x)=\displaystyle\sum_{i=0}^{\lfloor x \rfloor} \frac {-\theta^i}{iln (1- \theta)}

·       Parameter restrictions:

0 < θ < 1

·       Domain: 

x = {0,1,2,3, ...}

·       Mean:

 \frac {\theta}{(\theta - 1)ln(1- \theta)}

·       Mode: 

1

·       Variance:

\mu [(1- \theta)^{-1} - \mu]

 


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