# laplace: The Laplace (Double Exponential) Distribution In bda: Density Estimation for Grouped Data

## Description

Density, distribution function, quantile function and random generation for the Laplace (double exponential) distribution with mean `mu` and rate `rate` (i.e., mean `1/rate`).

## Usage

 ```1 2 3 4 5``` ```dlap(x, mu=0, rate=1) plap(q, mu=0, rate=1) qlap(p, mu=0, rate=1) rlap(n, mu=0, rate=1) fitlap(x,mu) ```

## 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. `mu` vector of means. `rate` vector of rates.

## Details

If `mu` is not specified, it assumes the default value of `0`.

If `rate` is not specified, it assumes the default value of `1`.

## Value

`dlap` gives the density, `plap` gives the distribution function, `qlap` gives the quantile function, and `rlap` generates random deviates.

`exp` for the exponential function.
Distributions for other standard distributions, including `dgamma` for the gamma distribution and `dexp` for the exponential distribution. `dweibull` for the Weibull distribution, both of which generalize the exponential.
 ```1 2 3 4 5 6 7 8 9``` ``` dlap(100) x <- rlap(1000,mu=0, rate=0.5) x0 = seq(-7,7, length=100) fitlap(x) plot(density(x), xlim=c(-7,7), ylim=c(0,0.35)) (out = fitlap(x)) lines(dlap(x0, out\$mu, out\$rate)~x0, col=2, lty=2) (out = fitlap(x, mu=0)) lines(dlap(x0, out\$mu, out\$rate)~x0, col=4, lty=2) ```