actuar: InversePareto – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

InversePareto

The Inverse Pareto Distribution

Description

Density function, distribution function, quantile function, random generation raw moments and limited moments for the Inverse Pareto distribution with parameters shape and scale.

Usage

dinvpareto(x, shape, scale, log = FALSE)
pinvpareto(q, shape, scale, lower.tail = TRUE, log.p = FALSE)
qinvpareto(p, shape, scale, lower.tail = TRUE, log.p = FALSE)
rinvpareto(n, shape, scale)
minvpareto(order, shape, scale)
levinvpareto(limit, shape, scale, 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.
`shape, scale`	parameters. Must be strictly positive.
`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 Pareto distribution with parameters shape = a and scale = s has density:

f(x) = a s x^(a - 1)/(x + s)^(a + 1)

for x > 0, a > 0 and s > 0.

The kth raw moment of the random variable X is E[X^k], -shape < k < 1.

The kth limited moment at some limit d is E[min(X, d)^k], k > -shape.

Value

dinvpareto gives the density, pinvpareto gives the distribution function, qinvpareto gives the quantile function, rinvpareto generates random deviates, minvpareto gives the kth raw moment, and levinvpareto calculates the kth limited moment.

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

Note

Evaluation of levinvpareto is done using numerical integration.

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(dinvpareto(2, 3, 4, log = TRUE))
p <- (1:10)/10
pinvpareto(qinvpareto(p, 2, 3), 2, 3)
minvpareto(0.5, 1, 2)

actuar

Actuarial Functions and Heavy Tailed Distributions

v3.1-2

GPL (>= 2)

Authors

Vincent Goulet [cre, aut], Sébastien Auclair [ctb], Christophe Dutang [aut], Nicholas Langevin [ctb], Xavier Milhaud [ctb], Tommy Ouellet [ctb], Alexandre Parent [ctb], Mathieu Pigeon [aut], Louis-Philippe Pouliot [ctb], Jeffrey A. Ryan [aut] (Package API), Robert Gentleman [aut] (Parts of the R to C interface), Ross Ihaka [aut] (Parts of the R to C interface), R Core Team [aut] (Parts of the R to C interface), R Foundation [aut] (Parts of the R to C interface)

Initial release

2021-03-30