Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ Gamma distribution ▷ Probability density function

Theorem: Let $X$ be a positive random variable following a gamma distribution:

$\label{eq:gam} X \sim \mathrm{Gam}(a, b) \; .$

Then, the probability density function of $X$ is

$\label{eq:gam-pdf} f_X(x) = \frac{b^a}{\Gamma(a)} x^{a-1} \exp[-b x] \; .$

Proof: This follows directly from the definition of the gamma distribution.

Sources:

Metadata: ID: P45 | shortcut: gam-pdf | author: JoramSoch | date: 2020-02-08, 23:41.