distributions3 (version 0.2.1)

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)

Value

An Exponential object.

Arguments

rate

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

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, $\mathrm{\infty }$)

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):

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

See Also

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

Examples

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))