Create an Erlang distribution

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
#> [1] "Erlang(k = 5, lambda = 2)"

random(X, 10)
#>  [1] 4.727510 3.628168 1.512156 4.771854 2.257310 3.645070 5.083710 2.509344
#>  [9] 1.093361 2.021506

pdf(X, 2)
#> [1] 0.3907336
log_pdf(X, 2)
#> [1] -0.9397292

cdf(X, 4)
#> [1] 0.9003676
quantile(X, 0.7)
#> [1] 2.945181

cdf(X, quantile(X, 0.7))
#> [1] 0.7
quantile(X, cdf(X, 7))
#> [1] 7