Continuous random variable

Gamma distribution

A gamma distributed random variable where is described by the probability density function prob

where is the gamma function.

Properties

1. Expectation:
2. Variance:
3. Moments: for

Furthermore

1. The sum of independent exponential random variables is
2. Conjugate prior to Poisson elaborate
3. A special case is the Chi-squared distribution

Relationship to other distributions

• By the Central limits theorem for integer , as .

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