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

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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 ≤ 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) = (a*b^a) / x^(a+1)

Cumulative distribution function

F(x) = 1 - (b/x)^a

Quantile function

F^-1(p) = b/(1-p)^(1-a)

## References

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

## Examples

 ```1 2 3 4 5 6``` ```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 Sept. 7, 2020, 5:09 p.m.