boostmath (version 1.4.0)

bernoulli_distribution: Bernoulli Distribution Functions

Description

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

Usage

bernoulli_distribution(p_success)
bernoulli_pdf(x, p_success)
bernoulli_lpdf(x, p_success)
bernoulli_cdf(x, p_success)
bernoulli_lcdf(x, p_success)
bernoulli_quantile(p, p_success)

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

p_success

probability of success (0 <= p_success <= 1)

x

quantile (0 or 1)

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Bernoulli distribution with p_success = 0.5
dist <- bernoulli_distribution(0.5)
# 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
bernoulli_pdf(1, 0.5)
bernoulli_lpdf(1, 0.5)
bernoulli_cdf(1, 0.5)
bernoulli_lcdf(1, 0.5)
bernoulli_quantile(0.5, 0.5)