Erlang: Create an Erlang distribution

In distributions3: Probability Distributions as S3 Objects

Create an Erlang distribution

Description

The Erlang distribution is a two-parameter family of continuous probability distributions with support x \in [0,\infty). The two parameters are a positive integer shape parameter k and a positive real rate parameter \lambda. The Erlang distribution with shape parameter k = 1 simplifies to the exponential distribution, and it is a special case of the gamma distribution. It corresponds to a sum of k independent exponential variables with mean 1 / \lambda each.

Usage

Erlang(k, lambda)

Arguments

k	The shape parameter. Can be any positive integer number.
lambda	The rate parameter. Can be any positive number.

Value

An Erlang object.

See Also

Other continuous distributions: Beta(), Cauchy(), ChiSquare(), Exponential(), FisherF(), Frechet(), GEV(), GP(), Gamma(), Gumbel(), LogNormal(), Logistic(), Normal(), RevWeibull(), StudentsT(), Tukey(), Uniform(), Weibull()

Examples

set.seed(27)

X <- Erlang(5, 2)
X

random(X, 10)

pdf(X, 2)
log_pdf(X, 2)

cdf(X, 4)
quantile(X, 0.7)

cdf(X, quantile(X, 0.7))
quantile(X, cdf(X, 7))

distributions3 documentation built on Sept. 30, 2024, 9:37 a.m.