RTDE (version 0.2-2)

upareto: The unit Pareto Distribution

Description

Density function, distribution function, quantile function, random generation.

Usage

dupareto(x, log = FALSE)
pupareto(q, lower.tail=TRUE, log.p = FALSE)
qupareto(p, lower.tail=TRUE, log.p = FALSE)
rupareto(n)

Value

dupareto gives the density,

pupareto gives the distribution function,

qupareto gives the quantile function, and

rupareto generates random deviates.

The length of the result is determined by n for

rupareto, and is the maximum of the lengths of the numerical parameters for the other functions.

The numerical parameters other than n are recycled to the length of the result. Only the first elements of the logical parameters are used.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

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, \(P[X > x]\).

Author

Christophe Dutang

Details

The extended Pareto distribution is defined by the following density and distribution function $$ f(x) = \frac{1}{x^2}, F(x) = 1-\frac{1}{x}, $$ for all \(x>0\).

References

Johnson, N.L., Kotz, S. and Balakrishnan, N. (2000), Continuous Univariate Distributions, Volume 1, Second Edition, John Wiley and Sons.

Examples

#####
# (1) density function
x <- seq(0, 5, length=24)

cbind(x, dupareto(x))

#####
# (2) distribution function

cbind(x, pupareto(x))