rmutil (version 1.1.0)

Pareto: Pareto Distribution

Description

These functions provide information about the Pareto distribution with location parameter equal to m and dispersion equal to s: density, cumulative distribution, quantiles, log hazard, and random generation.

The Pareto distribution has density $$ f(y) = \frac{\sigma }{\mu (\sigma-1)(1 + y/(\mu (\sigma-1)))^{\sigma+1}}$$ where \(\mu\) is the mean parameter of the distribution and \(\sigma\) is the dispersion.

This distribution can be obtained as a mixture distribution from the exponential distribution using a gamma mixing distribution.

Usage

dpareto(y, m, s, log=FALSE)
ppareto(q, m, s)
qpareto(p, m, s)
rpareto(n, m, s)

Arguments

y

vector of responses.

q

vector of quantiles.

p

vector of probabilities

n

number of values to generate

m

vector of location parameters.

s

vector of dispersion parameters.

log

if TRUE, log probabilities are supplied.

See Also

dexp for the exponential distribution.

Examples

# NOT RUN {
dpareto(5, 2, 2)
ppareto(5, 2, 2)
qpareto(0.9, 2, 2)
rpareto(10, 2, 2)
# }