# PowerDist: Power distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```dpower(x, alpha, beta, log = FALSE) ppower(q, alpha, beta, lower.tail = TRUE, log.p = FALSE) qpower(p, alpha, beta, lower.tail = TRUE, log.p = FALSE) rpower(n, alpha, beta) ```

## Arguments

 `x, q` vector of quantiles. `alpha, beta` 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) = (β*x^(β-1)) / (α^β)

Cumulative distribution function

F(x) = x^β / α^β

Quantile function

F^-1(p) = α * p^(1/β)

## Examples

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

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