16.10 Rayleigh Distribution
16.10.1 Probability Density Function
If \(\sigma \in \mathbb{R}^+\), then for \(y \in [0,\infty)\), \[ \text{Rayleigh}(y|\sigma) = \frac{y}{\sigma^2} \exp(-y^2 / 2\sigma^2) \!. \]
16.10.2 Sampling Statement
y ~ rayleigh(sigma)
Increment target log probability density with rayleigh_lpdf(y | sigma) dropping constant additive terms.
16.10.3 Stan Functions
real rayleigh_lpdf(reals y | reals sigma)
The log of the Rayleigh density of y given scale sigma
real rayleigh_cdf(real y, real sigma)
The Rayleigh cumulative distribution of y given scale sigma
real rayleigh_lcdf(real y | real sigma)
The log of the Rayleigh cumulative distribution of y given scale sigma
real rayleigh_lccdf(real y | real sigma)
The log of the Rayleigh complementary cumulative distribution of y given scale sigma
R rayleigh_rng(reals sigma)
Generate a Rayleigh variate with scale sigma; may only be used in generated quantities block. For a description of argument and return types, see section vectorized PRNG functions.