boostmath (version 1.4.0)

arcsine_distribution: Arcsine Distribution Functions

Description

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

Usage

arcsine_distribution(x_min = 0, x_max = 1)
arcsine_pdf(x, x_min = 0, x_max = 1)
arcsine_lpdf(x, x_min = 0, x_max = 1)
arcsine_cdf(x, x_min = 0, x_max = 1)
arcsine_lcdf(x, x_min = 0, x_max = 1)
arcsine_quantile(p, x_min = 0, x_max = 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

x_min

minimum value of the distribution (default is 0)

x_max

maximum value of the distribution (default is 1)

x

quantile

p

probability

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Arcsine distribution with default parameters
dist <- arcsine_distribution()
# 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)
range(dist)
quantile(dist, 0.2)
standard_deviation(dist)
support(dist)
variance(dist)
skewness(dist)
kurtosis(dist)
kurtosis_excess(dist)

# Convenience functions
arcsine_pdf(0.5)
arcsine_lpdf(0.5)
arcsine_cdf(0.5)
arcsine_lcdf(0.5)
arcsine_quantile(0.5)