Logarithmic equations

· Format:

Logarithmic (θ)

· Probability mass function:

$\begin{array}{l}\displaystyle f(x)= \frac {-\theta^x}{xln (1- \theta)}\end{array}$

· Cumulative distribution function:

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

· Parameter restrictions:

0 < θ < 1

· Domain:

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

· Mean:

$\begin{array}{l}\displaystyle \frac {\theta}{(\theta - 1)ln(1- \theta)}\end{array}$

· Mode:

1

· Variance:

$\begin{array}{l}\mu [(1- \theta)^{-1} - \mu]\end{array}$

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