# Lomax: Lomax distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```dlomax(x, lambda, kappa, log = FALSE) plomax(q, lambda, kappa, lower.tail = TRUE, log.p = FALSE) qlomax(p, lambda, kappa, lower.tail = TRUE, log.p = FALSE) rlomax(n, lambda, kappa) ```

## Arguments

 `x, q` vector of quantiles. `lambda, kappa` positive valued parameters. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ 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) = λ*κ / (1+λ*x)^(κ+1)

Cumulative distribution function

F(x) = 1-(1+λ*x)^-κ

Quantile function

F^-1(p) = ((1-p)^(-1/κ)-1) / λ

## Examples

 ```1 2 3 4 5 6``` ```x <- rlomax(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dlomax(x, 5, 16), 0, 1, col = "red", add = TRUE, n = 5000) hist(plomax(x, 5, 16)) plot(ecdf(x)) curve(plomax(x, 5, 16), 0, 1, col = "red", lwd = 2, add = TRUE) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.