Statistics - Log Gamma Distribution

Log Gamma Distribution is a probability density function with positive shape parameters $ {\alpha, \beta } $ and location parameter $ { \mu } $. It is defined by following formula.


${ f(x) = \frac{e^{\beta x}e^{\frac{-e^x}{\alpha}}}{ \alpha^\beta \Gamma(\beta)} \\[7pt] \, where -\infty \gt x \lt \infty }$

Where −

  • ${\alpha}$ = positive shape parameter.

  • ${\beta}$ = positive shape parameter.

  • ${x}$ = random variable.

Following diagram shows the probability density function with three different parameter combinations.

Log Gamma Distribution
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