InversePareto {actuar}R Documentation

The Inverse Pareto Distribution

Description

Density, 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] and the k limited moment at some limit d is E[min(X, d)].

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.

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

[Package actuar version 0.9-3 Index]