boostmath (version 1.4.0)

normal_distribution: Normal Distribution Functions

Description

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

Usage

normal_distribution(mean = 0, sd = 1)
normal_pdf(x, mean = 0, sd = 1)
normal_lpdf(x, mean = 0, sd = 1)
normal_cdf(x, mean = 0, sd = 1)
normal_lcdf(x, mean = 0, sd = 1)
normal_quantile(p, mean = 0, sd = 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

mean

mean parameter (default is 0)

sd

standard deviation parameter (default is 1)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Normal distribution with mean = 0, sd = 1
dist <- normal_distribution(0, 1)
# 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
normal_pdf(0)
normal_lpdf(0)
normal_cdf(0)
normal_lcdf(0)
normal_quantile(0.5)