actuar (version 3.3-4)

InverseExponential: The Inverse Exponential Distribution

Description

Density function, distribution function, quantile function, random generation raw moments and limited moments for the Inverse Exponential distribution with parameter scale.

Usage

dinvexp(x, rate = 1, scale = 1/rate, log = FALSE)
pinvexp(q, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qinvexp(p, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rinvexp(n, rate = 1, scale = 1/rate)
minvexp(order, rate = 1, scale = 1/rate)
levinvexp(limit, rate = 1, scale = 1/rate, order)

Value

dinvexp gives the density,

pinvexp gives the distribution function,

qinvexp gives the quantile function,

rinvexp generates random deviates,

minvexp gives the \(k\)th raw moment, and

levinvexp calculates the \(k\)th limited moment.

Invalid arguments will result in return value NaN, with a warning.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

scale

parameter. Must be strictly positive.

rate

an alternative way to specify the scale.

log, log.p

logical; if TRUE, probabilities/densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

order

order of the moment.

limit

limit of the loss variable.

Author

Vincent Goulet and Mathieu Pigeon

Details

The inverse exponential distribution with parameter scale \(= \theta\) has density: $$f(x) = \frac{\theta e^{-\theta/x}}{x^2}$$ for \(x > 0\) and \(\theta > 0\).

The \(k\)th raw moment of the random variable \(X\) is \(E[X^k]\), \(k < 1\), and the \(k\)th limited moment at some limit \(d\) is \(E[\min(X, d)^k]\), all \(k\).

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

Examples

exp(dinvexp(2, 2, log = TRUE))
p <- (1:10)/10
pinvexp(qinvexp(p, 2), 2)
minvexp(0.5, 2)