boostmath (version 1.4.0)

poisson_distribution: Poisson Distribution Functions

Description

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

Usage

poisson_distribution(lambda = 1)
poisson_pdf(x, lambda = 1)
poisson_lpdf(x, lambda = 1)
poisson_cdf(x, lambda = 1)
poisson_lcdf(x, lambda = 1)
poisson_quantile(p, lambda = 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

lambda

rate parameter (default is 1)

x

quantile

p

probability (0 <= p <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Poisson distribution with lambda = 1
dist <- poisson_distribution(1)
# Apply generic functions
cdf(dist, 5)
logcdf(dist, 5)
pdf(dist, 5)
logpdf(dist, 5)
hazard(dist, 5)
chf(dist, 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
poisson_pdf(0, 1)
poisson_lpdf(0, 1)
poisson_cdf(0, 1)
poisson_lcdf(0, 1)
poisson_quantile(0.5, 1)