InverseExponential {actuar}

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.

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

Value

dinvexp gives the density, pinvexp gives the distribution function, qinvexp gives the quantile function, rinvexp generates random deviates, minvexp gives the kth raw moment, and levinvexp calculates the kth limited moment.

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

Note

levinvexp computes the limited expected value using gammainc from package expint.

The "distributions" package vignette provides the interrelations between the continuous size distributions in actuar and the complete formulas underlying the above functions.

Author(s)

Vincent Goulet [e-mail] and Mathieu Pigeon

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)