dist_exponential: The Exponential Distribution

In distributional: Vectorised Probability Distributions

The Exponential Distribution

Description

Exponential distributions are frequently used to model waiting times and the time between events in a Poisson process.

Usage

dist_exponential(rate)

Arguments

rate	vector of rates.

Details

We recommend reading this documentation on pkgdown which renders math nicely. https://pkg.mitchelloharawild.com/distributional/reference/dist_exponential.html

In the following, let X be an Exponential random variable with parameter rate = \lambda.

Support: x \in [0, \infty)

Mean: \frac{1}{\lambda}

Variance: \frac{1}{\lambda^2}

Probability density function (p.d.f):

f(x) = \lambda e^{-\lambda x}

Cumulative distribution function (c.d.f):

F(x) = 1 - e^{-\lambda x}

Moment generating function (m.g.f):

E(e^{tX}) = \frac{\lambda}{\lambda - t}, \quad t < \lambda

See Also

stats::Exponential

Examples

dist <- dist_exponential(rate = c(2, 1, 2/3))

dist
mean(dist)
variance(dist)
skewness(dist)
kurtosis(dist)

generate(dist, 10)

density(dist, 2)
density(dist, 2, log = TRUE)

cdf(dist, 4)

quantile(dist, 0.7)

distributional documentation built on June 27, 2026, 5:06 p.m.