Cauchy Distribution Functions

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

Usage

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)

Arguments

x

quantile

location

location parameter (default is 0)

scale

scale parameter (default is 1)

p

probability (0 <= p <= 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

# Cauchy distribution with location = 0, scale = 1
cauchy_pdf(0)
#> [1] 0.3183099
cauchy_lpdf(0)
#> [1] -1.14473
cauchy_cdf(0)
#> [1] 0.5
cauchy_lcdf(0)
#> [1] -0.6931472
cauchy_quantile(0.5)
#> [1] 0