actuar (version 0.9-4)

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)

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.

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.

Details

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

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

For numerical evaluation purposes, levinvexp requires that order < 1.

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.

Examples

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