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)

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.

vector of probabilities.

number of observations.

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.

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

# NOT RUN {
dpareto(seq(1, 5), 1, 1)
qpareto(ppareto(seq(1, 5), 1, 1), 1 ,1)
rpareto(5, 1, 1)
# }