boostmath (version 1.4.0)

beta_distribution: Beta Distribution Functions

Description

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

Usage

beta_distribution(alpha, beta)
beta_pdf(x, alpha, beta)
beta_lpdf(x, alpha, beta)
beta_cdf(x, alpha, beta)
beta_lcdf(x, alpha, beta)
beta_quantile(p, alpha, beta)
beta_find_alpha(mean = NULL, variance = NULL, beta = NULL, x = NULL, p = NULL)
beta_find_beta(mean = NULL, variance = NULL, alpha = NULL, x = NULL, p = NULL)

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

alpha

shape parameter (alpha > 0)

beta

shape parameter (beta > 0)

x

quantile (0 <= x <= 1)

p

probability (0 <= p <= 1)

mean

Mean of the Beta distribution

variance

Variance of the Beta distribution

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Beta distribution with shape parameters alpha = 2, beta = 5
dist <- beta_distribution(2, 5)
# 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)
skewness(dist)
kurtosis(dist)
kurtosis_excess(dist)

# Convenience functions
beta_pdf(0.5, 2, 5)
beta_lpdf(0.5, 2, 5)
beta_cdf(0.5, 2, 5)
beta_lcdf(0.5, 2, 5)
beta_quantile(0.5, 2, 5)

if (FALSE) {
# Find alpha given mean and variance
beta_find_alpha(mean = 0.3, variance = 0.02)
# Find alpha given beta, x, and probability
beta_find_alpha(beta = 5, x = 0.4, p = 0.6)
# Find beta given mean and variance
beta_find_beta(mean = 0.3, variance = 0.02)
# Find beta given alpha, x, and probability
beta_find_beta(alpha = 2, x = 0.4, p = 0.6)
}