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.
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)
#> [1] 0.6475836
logcdf(dist, 0.5)
#> [1] -0.4345074
pdf(dist, 0.5)
#> [1] 0.2546479
logpdf(dist, 0.5)
#> [1] -1.367873
hazard(dist, 0.5)
#> [1] 0.7225768
chf(dist, 0.5)
#> [1] 1.042942
median(dist)
#> [1] 0
mode(dist)
#> [1] 0
range(dist)
#> [1] -Inf Inf
quantile(dist, 0.2)
#> [1] -1.376382
support(dist)
#> [1] -Inf Inf
# Convenience functions
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