Pareto distribution

Density, distribution function, quantile function, and random generation for the pareto distribution.

Usage

dpareto(x, mu = 1, log = FALSE)

ppareto(q, mu = 1, lower.tail = TRUE, log.p = FALSE)

qpareto(p, mu = 1, lower.tail = TRUE, log.p = FALSE)

rpareto(n, mu = 1)

Arguments

x, q

vector of quantiles

mu

location parameter, must be positive.

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise \(P[X > x]\).

p

vector of probabilities

n

number of random values to return

Value

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and rpareto generates random deviates.

Details

This implementation of dpareto and ppareto allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package. See gamlss.dist::PARETO for more details.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

set.seed(123)
x <- rpareto(1, mu = 5)
d <- dpareto(x, mu = 5)
p <- ppareto(x, mu = 5)
q <- qpareto(p, mu = 5)