Description Usage Arguments Details Value Warning See Also Examples

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

and scale parameter `scale`

.

1 2 3 4 |

`x,q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of samples to generate. |

`loc` |
vector of location parameters. |

`scale` |
vector of scale parameters. These must be positive. |

`lower.tail` |
logical; if TRUE (default), probabilities are |

`log,log.p` |
logical; if TRUE, probabilities |

If `loc`

or `scale`

are not specified, they assume the default values of 0 and 1 respectively.

The Laplace distribution has density

*f(x) = \exp(- |x-μ|/σ)/(2σ)*

where *μ* is the location parameter and *σ* is the scale parameter.

`dlapl`

gives the density, `plapl`

gives the distribution function, `qlapl`

gives the quantile function, and `rlapl`

generates random deviates.

The length of the result is determined by `n`

in `rlapl`

, and is the maximum of the lengths of the numerical arguments for the other functions. Standard `R`

vector operations are to be assumed.

If `sd`

=0, the limit as `sd`

decreases to 0 is returned, i.e., a point mass at `loc`

. The case `sd`

<0 is an error and nothing is returned.

Some checks are done previous to standard evaluation, but vector computations have not yet been tested thoroughly! Typically vectors not having lengths multiple of each other return an error.

dexp for the exponential distribution which is the positive part of the Laplace distribution.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## evaluate the density function on a grid of values
x <- seq(from=-5, to=5, by=0.1)
fx <- dlapl(x, loc=1, scale=.5)
## generate random samples of a mixture of Laplace distributions
rnd <- rlapl(1000, loc=c(-5,-3,2), scale=0.5)
## an alternative:
rnd <- runif(1000)
rnd <- qlapl(rnd, loc=c(-5,-3,2), scale=0.5)
## integrate the Laplace density on [a,b]
a <- -1
b <- 7
integral <- plapl(b)-plapl(a)
``` |

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