distributions3 (version 0.1.2)

Exponential: Create an Exponential distribution

Description

Exponential distributions are frequently used for modeling the amount of time that passes until a specific event occurs. For example, exponential distributions could be used to model the time between two earthquakes, the amount of delay between internet packets, or the amount of time a piece of machinery can run before needing repair.

Usage

Exponential(rate = 1)

Arguments

rate

The rate parameter, written \(\lambda\) in textbooks. Can be any positive number. Defaults to 1.

Value

An Exponential object.

Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail and much greater clarity.

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

Support: x in [0, \(\infty\))

Mean: 1 / \(\lambda\)

Variance: 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):

$$ \frac{\lambda}{\lambda - t}, for t < \lambda $$

See Also

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

Examples

# NOT RUN {
set.seed(27)

X <- Exponential(5)
X

mean(X)
variance(X)
skewness(X)
kurtosis(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))
# }