Gamma distribution and when it appears.

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Answer

$X ~ Gamma(k, θ): support (0, \infty).$
$PDF \propto x^(k-1) * e^(-x/θ).$
$\operatorname{Var}\; = \;k{\theta}^{2}$
$\mathrm{Exponential}\; = \;\Gamma(1, \;{\theta})$
$Uses: waiting time until k events in Poisson process, survival times, Bayesian conjugate prior for Poisson rate and normal precision.$
$Common as a heavy-tailed regression target (Gamma GLM for positive continuous outcomes: durations, insurance claims).$

Check yourself — multiple choice

Negative support
Positive support, sum of k Exp(1/θ); conjugate prior for Poisson rate; used in GLMs for positive continuous outcomes
Same as normal
Var = k

Gamma: positive support, waiting times for k Poisson events, GLM for durations.

#distributions#bayesian

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