Exponential | R Documentation |
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.
Exponential(rate = 1)
rate |
The rate parameter, written λ in textbooks.
Can be any positive number. Defaults to |
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
= λ.
Support: x in [0, ∞)
Mean: 1 / λ
Variance: 1 / λ^2
Probability density function (p.d.f):
f(x) = λ e^{-λ x}
Cumulative distribution function (c.d.f):
F(x) = 1 - e^{-λ x}
Moment generating function (m.g.f):
\frac{λ}{λ - t}, for t < λ
An Exponential
object.
Other continuous distributions:
Beta()
,
Cauchy()
,
ChiSquare()
,
Erlang()
,
FisherF()
,
Frechet()
,
GEV()
,
GP()
,
Gamma()
,
Gumbel()
,
LogNormal()
,
Logistic()
,
Normal()
,
RevWeibull()
,
StudentsT()
,
Tukey()
,
Uniform()
,
Weibull()
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))
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.