16.5 Exponential Distribution
16.5.1 Probability Density Function
If \(\beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{Exponential}(y|\beta) = \beta \, \exp ( - \beta \, y ) . \]
16.5.2 Sampling Statement
y ~ exponential(beta)
Increment target log probability density with exponential_lpdf(y | beta) dropping constant additive terms.
16.5.3 Stan Functions
real exponential_lpdf(reals y | reals beta)
The log of the exponential density of y given inverse scale beta
real exponential_cdf(reals y, reals beta)
The exponential cumulative distribution function of y given inverse scale beta
real exponential_lcdf(reals y | reals beta)
The log of the exponential cumulative distribution function of y given inverse scale beta
real exponential_lccdf(reals y | reals beta)
The log of the exponential complementary cumulative distribution function of y given inverse scale beta
R exponential_rng(reals beta)
Generate an exponential variate with 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.