R: The Inverse Exponential Distribution

InverseExponential {actuar} | R Documentation

## 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 <= 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.

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 vincent.goulet@act.ulaval.ca 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)

[Package actuar version 3.0-0 Index]