This is an old version, view current version.

## 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