17.5 Exponential distribution
17.5.1 Probability density function
If \(\beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{Exponential}(y|\beta) = \beta \, \exp ( - \beta \, y ) . \]
17.5.2 Sampling statement
y ~
exponential
(beta)
Increment target log probability density with exponential_lupdf(y | beta)
.
17.5.3 Stan functions
real
exponential_lpdf
(reals y | reals beta)
The log of the exponential density of y given inverse scale beta
real
exponential_lupdf
(reals y | reals beta)
The log of the exponential density of y given inverse scale beta
dropping constant additive terms
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.