boostmath (version 1.4.0)

triangular_distribution: Triangular Distribution Functions

Description

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

Usage

triangular_distribution(lower = -1, mode = 0, upper = 1)
triangular_pdf(x, lower = -1, mode = 0, upper = 1)
triangular_lpdf(x, lower = -1, mode = 0, upper = 1)
triangular_cdf(x, lower = -1, mode = 0, upper = 1)
triangular_lcdf(x, lower = -1, mode = 0, upper = 1)
triangular_quantile(p, lower = -1, mode = 0, upper = 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

lower

lower limit of the distribution (default is -1)

mode

mode of the distribution (default is 0)

upper

upper limit of the distribution (default is 1)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Triangular distribution with lower = -1, mode = 0, upper = 1
dist <- triangular_distribution(-1, 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
triangular_pdf(1)
triangular_lpdf(1)
triangular_cdf(1)
triangular_lcdf(1)
triangular_quantile(0.5)