Pareto: Pareto distribution

In extraDistr: Additional Univariate and Multivariate Distributions

Pareto distribution

Description

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

Usage

dpareto(x, a = 1, b = 1, log = FALSE)

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

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

rpareto(n, a = 1, b = 1)

Arguments

x, q	vector of quantiles.
a, b	positive valued scale and location parameters.
log, log.p	logical; if TRUE, probabilities p are given 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 observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function

f(x) = \frac{ab^a}{x^{a+1}}

Cumulative distribution function

F(x) = 1 - \left(\frac{b}{x}\right)^a

Quantile function

F^{-1}(p) = \frac{b}{(1-p)^{1-a}}

References

Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC

Examples

x <- rpareto(1e5, 5, 16)
hist(x, 100, freq = FALSE)
curve(dpareto(x, 5, 16), 0, 200, col = "red", add = TRUE)
hist(ppareto(x, 5, 16))
plot(ecdf(x))
curve(ppareto(x, 5, 16), 0, 200, col = "red", lwd = 2, add = TRUE)

extraDistr documentation built on May 29, 2024, 9:31 a.m.