boostmath (version 1.4.0)

rayleigh_distribution: Rayleigh Distribution Functions

Description

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Rayleigh distribution.

Usage

rayleigh_distribution(sigma = 1)
rayleigh_pdf(x, sigma = 1)
rayleigh_lpdf(x, sigma = 1)
rayleigh_cdf(x, sigma = 1)
rayleigh_lcdf(x, sigma = 1)
rayleigh_quantile(p, sigma = 1)

Value

A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.

Arguments

sigma

scale parameter (default is 1)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Rayleigh distribution with sigma = 1
dist <- rayleigh_distribution(1)
# Apply generic functions
cdf(dist, 0.5)
logcdf(dist, 0.5)
pdf(dist, 0.5)
logpdf(dist, 0.5)
hazard(dist, 0.5)
chf(dist, 0.5)
mean(dist)
median(dist)
mode(dist)
range(dist)
quantile(dist, 0.2)
standard_deviation(dist)
support(dist)
variance(dist)
skewness(dist)
kurtosis(dist)
kurtosis_excess(dist)

# Convenience functions
rayleigh_pdf(1)
rayleigh_lpdf(1)
rayleigh_cdf(1)
rayleigh_lcdf(1)
rayleigh_quantile(0.5)