boostmath (version 1.4.0)

holtsmark_distribution: Holtsmark Distribution Functions

Description

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

Usage

holtsmark_distribution(location = 0, scale = 1)
holtsmark_pdf(x, location = 0, scale = 1)
holtsmark_lpdf(x, location = 0, scale = 1)
holtsmark_cdf(x, location = 0, scale = 1)
holtsmark_lcdf(x, location = 0, scale = 1)
holtsmark_quantile(p, location = 0, 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

location

location parameter (default is 0)

scale

scale parameter (default is 1)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Holtsmark distribution with location 0 and scale 1
dist <- holtsmark_distribution(0, 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)

# Convenience functions
holtsmark_pdf(3)
holtsmark_lpdf(3)
holtsmark_cdf(3)
holtsmark_lcdf(3)
holtsmark_quantile(0.5)