Pareto: The Pareto distribution

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

The Pareto distribution

Description

Density, distribution function, quantile function and random generation for the Pareto distribution (type I).

Usage

dpareto(x, shape, scale = 1, log = FALSE)
ppareto(x, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
qpareto(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
rpareto(n, shape, scale = 1)

Arguments

x	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations.
shape	The shape parameter of the Pareto distribution, a strictly positive number.
scale	The scale parameter of the Pareto distribution, a strictly positive number. Its default value is 1.
log	Logical indicating if the densities are given as \log(f), default is FALSE.
lower.tail	Logical indicating if the probabilities are of the form P(X\le x) (TRUE) or P(X>x) (FALSE). Default is TRUE.
log.p	Logical indicating if the probabilities are given as \log(p), default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the Pareto distribution is equal to F(x) = 1-(x/scale)^{-shape} for all x \ge scale and F(x)=0 otherwise. Both shape and scale need to be strictly positive.

Value

dpareto gives the density function evaluated in x, ppareto the CDF evaluated in x and qpareto the quantile function evaluated in p. The length of the result is equal to the length of x or p.

rpareto returns a random sample of length n.

Author(s)

Tom Reynkens.

See Also

tPareto, GPD, Distributions

Examples

# Plot of the PDF
x <- seq(1, 10, 0.01)
plot(x, dpareto(x, shape=2), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(1, 10, 0.01)
plot(x, ppareto(x, shape=2), xlab="x", ylab="CDF", type="l")

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.