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## 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.