InverseExponential {actuar}R Documentation

The Inverse Exponential Distribution

Description

Density, 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 = 1)

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 <= x], otherwise, P[X > x].
order order of the moment.
limit limit of the loss variable.

Details

The Inverse Exponential distribution with parameter scale = s has density:

f(x) = s exp(-s/x)/x^2

for x > 0 and s > 0.

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

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

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

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(-2, order = 3)

[Package actuar version 0.9-3 Index]