Pareto: The Pareto Distribution

Description

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

Usage

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

Value

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and

rpareto generates random deviates.

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

Arguments

x, q: vector of quantiles.
scale: scale parameter.
shape: shape parameter.
log, log.p: logical; if TRUE, probabilities $p$ are given as $log(p)$, default: FALSE.
lower.tail: logical; if TRUE, probabilities are $P[X \le x]$ otherwise, $P[X > x]$, default: TRUE.
p: vector of probabilities.
n: number of observations.

Details

The Pareto distribution function with scale parameter $s$ and shape parameter $\alpha$ has density given by $$f(x)=\alpha s^\alpha/x^(\alpha+1)$$ for $x\ge s$. The cumulative distribution function is $$F(x)=1-(s/x)^\alpha$$ for $x\ge s$. See https://en.wikipedia.org/wiki/Pareto_distribution for more details.

Examples

Run this code

dpareto(seq(1, 5), 1, 1)
qpareto(ppareto(seq(1, 5), 1, 1), 1 ,1)
rpareto(5, 1, 1)