boostmath (version 1.4.0)

gamma_distribution: Gamma Distribution Functions

Description

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

Usage

gamma_distribution(shape, scale = 1)
gamma_pdf(x, shape, scale = 1)
gamma_lpdf(x, shape, scale = 1)
gamma_cdf(x, shape, scale = 1)
gamma_lcdf(x, shape, scale = 1)
gamma_quantile(p, shape, scale = 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

shape

shape parameter (shape > 0)

scale

scale parameter (scale > 0)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Gamma distribution with shape = 3, scale = 4
dist <- gamma_distribution(3, 4)
# 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
gamma_pdf(2, 3, 4)
gamma_lpdf(2, 3, 4)
gamma_cdf(2, 3, 4)
gamma_lcdf(2, 3, 4)
gamma_quantile(0.5, 3, 4)