Pareto {mistr}

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.

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.

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.

See Also

paretodist

Examples

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