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17.6 Gamma distribution

17.6.1 Probability density function

If αR+ and βR+, then for yR+, Gamma(y|α,β)=βαΓ(α)yα1exp(βy).

17.6.2 Sampling statement

y ~ gamma(alpha, beta)

Increment target log probability density with gamma_lupdf(y | alpha, beta).

17.6.3 Stan functions

real gamma_lpdf(reals y | reals alpha, reals beta)
The log of the gamma density of y given shape alpha and inverse scale beta

real gamma_lupdf(reals y | reals alpha, reals beta)
The log of the gamma density of y given shape alpha and inverse scale beta dropping constant additive terms

real gamma_cdf(reals y, reals alpha, reals beta)
The cumulative gamma distribution function of y given shape alpha and inverse scale beta

real gamma_lcdf(reals y | reals alpha, reals beta)
The log of the cumulative gamma distribution function of y given shape alpha and inverse scale beta

real gamma_lccdf(reals y | reals alpha, reals beta)
The log of the complementary cumulative gamma distribution function of y given shape alpha and inverse scale beta

R gamma_rng(reals alpha, reals beta)
Generate a gamma variate with shape alpha and inverse scale beta; may only be used in transformed data and generated quantities blocks. For a description of argument and return types, see section vectorized PRNG functions.