18.5 Exponential distribution
18.5.1 Probability density function
If \(\beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{Exponential}(y|\beta) = \beta \, \exp ( - \beta \, y ) . \]
18.5.2 Sampling statement
y ~ exponential(beta)
Increment target log probability density with exponential_lupdf(y | beta).
Available since 2.0
18.5.3 Stan functions
real exponential_lpdf(reals y | reals beta)
The log of the exponential density of y given inverse scale beta
Available since 2.12
real exponential_lupdf(reals y | reals beta)
The log of the exponential density of y given inverse scale beta
dropping constant additive terms
Available since 2.25
real exponential_cdf(reals y, reals beta)
The exponential cumulative distribution function of y given inverse
scale beta
Available since 2.0
real exponential_lcdf(reals y | reals beta)
The log of the exponential cumulative distribution function of y given
inverse scale beta
Available since 2.12
real exponential_lccdf(reals y | reals beta)
The log of the exponential complementary cumulative distribution
function of y given inverse scale beta
Available since 2.12
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.
Available since 2.18