R: The Laplace distribution

Laplace {L1pack} | R Documentation

## The Laplace distribution

### Description

Density, distribution function, quantile function and random generation for the Laplace distribution with location parameter `location` and scale parameter `scale`.

### Usage

    dlaplace(x, location = 0, scale = 1, log = FALSE)
    plaplace(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
    qlaplace(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
    rlaplace(n, location = 0, scale = 1)

### Arguments

`x, q` | vector of quantiles.
`location, scale` | 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

If `location` or `scale` are not specified, they assume the default values of `0` and `1` respectively.

The Laplace distribution with location μ and scale φ has density

f(x) = 1/(φ√2) exp(-√2|x - μ|/φ)

### Value

`dlaplace`, `plaplace`, and `qlaplace` are respectively the density, distribution function and quantile function of the Laplace distribution. `rlaplace` generates random deviates from the Laplace.

The length of the result is determined by `n` for `rlaplace`, and is the maximum of the lengths of the numerical parameters for the other functions.

### Author(s)

Felipe Osorio and Tymoteusz Wolodzko

### References

Kotz, S., Kozubowski, T.J., and Podgorski, K. (2001). The Laplace Distributions and Generalizations. Birkhauser, Boston.

Phillips, R.F. (2002). Least absolute deviations estimation via the EM algorithm. Statistics and Computing 12, 281-285.

### See Also

Distributions for other standard distributions and `rmLaplace` for the random generation from the multivariate Laplace distribution.

### Examples

    x <- rlaplace(1000)
    ## Q-Q plot for Laplace data against true theoretical distribution:
    qqplot(qlaplace(ppoints(1000)), x, main = "Laplace Q-Q plot",
      xlab = "Theoretical quantiles", ylab = "Sample quantiles")
    abline(c(0,1), col = "red", lwd = 2)

[Package L1pack version 0.40 Index]