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.
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)
#> [1] 0.1175031
logcdf(dist, 0.5)
#> [1] -2.141291
pdf(dist, 0.5)
#> [1] 0.4412485
logpdf(dist, 0.5)
#> [1] -0.8181472
hazard(dist, 0.5)
#> [1] 0.5
chf(dist, 0.5)
#> [1] 0.125
mean(dist)
#> [1] 1.253314
median(dist)
#> [1] 1.17741
mode(dist)
#> [1] 1
range(dist)
#> [1] 0 Inf
quantile(dist, 0.2)
#> [1] 0.6680472
standard_deviation(dist)
#> [1] 0.6551364
support(dist)
#> [1] 0.000000e+00 1.797693e+308
variance(dist)
#> [1] 0.4292037
skewness(dist)
#> [1] 0.6311107
kurtosis(dist)
#> [1] 3.245089
kurtosis_excess(dist)
#> [1] 0.2450893
# Convenience functions
rayleigh_pdf(1)
#> [1] 0.6065307
rayleigh_lpdf(1)
#> [1] -0.5
rayleigh_cdf(1)
#> [1] 0.3934693
rayleigh_lcdf(1)
#> [1] -0.9327521
rayleigh_quantile(0.5)
#> [1] 1.17741