InversePareto: The Inverse Pareto Distribution

InverseParetoR Documentation

The Inverse Pareto Distribution


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


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)


x, q

vector of quantiles.


vector of probabilities.


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).


logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X > x].


order of the moment.


limit of the loss variable.


The inverse Pareto distribution with parameters shape = \tau and scale = \theta has density:

f(x) = \frac{\tau \theta x^{\tau - 1}}{% (x + \theta)^{\tau + 1}}

for x > 0, \tau > 0 and \theta > 0.

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

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


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.


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.


Vincent Goulet and Mathieu Pigeon


Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.


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

actuar documentation built on Nov. 8, 2023, 9:06 a.m.