boostmath (version 1.4.0)

cauchy_distribution: Cauchy Distribution Functions

Description

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

Usage

cauchy_distribution(location = 0, scale = 1)
cauchy_pdf(x, location = 0, scale = 1)
cauchy_lpdf(x, location = 0, scale = 1)
cauchy_cdf(x, location = 0, scale = 1)
cauchy_lcdf(x, location = 0, scale = 1)
cauchy_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

# Cauchy distribution with location = 0, scale = 1
dist <- cauchy_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)
median(dist)
mode(dist)
range(dist)
quantile(dist, 0.2)
support(dist)

# Convenience functions
cauchy_pdf(0)
cauchy_lpdf(0)
cauchy_cdf(0)
cauchy_lcdf(0)
cauchy_quantile(0.5)