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Pareto {actuar}

The Pareto Distribution
Package: 
actuar
Version: 
1.1-6

Description

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

Usage

dpareto(x, shape, scale, log = FALSE)
ppareto(q, shape, scale, lower.tail = TRUE, log.p = FALSE)
qpareto(p, shape, scale, lower.tail = TRUE, log.p = FALSE)
rpareto(n, shape, scale)
mpareto(order, shape, scale)
levpareto(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 Pareto distribution with parameters shape = a and scale = s has density: for x > 0, a > 0 and s > 0.

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

Values

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, rpareto generates random deviates, mpareto gives the kth raw moment, and levpareto gives the kth moment of the limited loss variable.

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

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2008), Loss Models, From Data to Decisions, Third Edition, Wiley.

Note

Distribution also known as the Pareto Type II or Lomax distribution.

Examples

exp(dpareto(2, 3, 4, log = TRUE))
p <- (1:10)/10
ppareto(qpareto(p, 2, 3), 2, 3)
mpareto(1, 2, 3)
levpareto(10, 2, 3, order = 1)

Author(s)

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

Documentation reproduced from package actuar, version 1.1-6. License: GPL (>= 2)