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

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```dlaplace(x, mu = 0, sigma = 1, log = FALSE) plaplace(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qlaplace(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rlaplace(n, mu = 0, sigma = 1) ```

## Arguments

 `x, q` vector of quantiles. `mu, sigma` location and scale parameters. Scale must be positive. `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) = 1/(2*σ) * exp(-|(x-μ)/σ|)

Cumulative distribution function

F(x) = [if x < mu:] 1/2 * exp((x-μ)/σ) [else:] 1 - 1/2 * exp((x-μ)/σ)

Quantile function

F^-1(p) = [if p < 0.5:] μ + σ * log(2*p) [else:] μ - σ * log(2*(1-p))

## References

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

Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.

## Examples

 ```1 2 3 4 5 6``` ```x <- rlaplace(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dlaplace(x, 5, 16), -200, 200, n = 500, col = "red", add = TRUE) hist(plaplace(x, 5, 16)) plot(ecdf(x)) curve(plaplace(x, 5, 16), -200, 200, n = 500, col = "red", lwd = 2, add = TRUE) ```

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