boostmath (version 1.4.0)

hyperexponential_distribution: Hyperexponential Distribution Functions

Description

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

Usage

hyperexponential_distribution(probabilities, rates)
hyperexponential_pdf(x, probabilities, rates)
hyperexponential_lpdf(x, probabilities, rates)
hyperexponential_cdf(x, probabilities, rates)
hyperexponential_lcdf(x, probabilities, rates)
hyperexponential_quantile(p, probabilities, rates)

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

probabilities

vector of probabilities (sum must be 1)

rates

vector of rates (all rates must be > 0)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Hyperexponential distribution with probabilities = c(0.5, 0.5) and rates = c(1, 2)
dist <- hyperexponential_distribution(c(0.5, 0.5), c(1, 2))
# 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
hyperexponential_pdf(2, c(0.5, 0.5), c(1, 2))
hyperexponential_lpdf(2, c(0.5, 0.5), c(1, 2))
hyperexponential_cdf(2, c(0.5, 0.5), c(1, 2))
hyperexponential_lcdf(2, c(0.5, 0.5), c(1, 2))
hyperexponential_quantile(0.5, c(0.5, 0.5), c(1, 2))