Description Usage Arguments Details Value Author(s) References See Also Examples

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

and scale parameter `scale`

.

1 2 3 4 |

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations.
Same as in |

`location` |
the location parameter |

`scale` |
the scale parameter |

`log` |
Logical.
If |

`lower.tail, log.p` |
Same meaning as in |

The Laplace distribution is often known as the double-exponential distribution and, for modelling, has heavier tail than the normal distribution. The Laplace density function is

*
f(y) = (1/(2b)) exp( -|y-a|/b ) *

where *-Inf<y<Inf*,
*-Inf<a<Inf* and
*b>0*.
The mean is *a* and the variance is *2b^2*.

See `laplace`

, the VGAM family function
for estimating the two parameters by maximum likelihood estimation,
for formulae and details.
Apart from `n`

, all the above arguments may be vectors and
are recyled to the appropriate length if necessary.

`dlaplace`

gives the density,
`plaplace`

gives the distribution function,
`qlaplace`

gives the quantile function, and
`rlaplace`

generates random deviates.

T. W. Yee and Kai Huang

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011).
*Statistical Distributions*,
Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
loc <- 1; b <- 2
y <- rlaplace(n = 100, loc = loc, scale = b)
mean(y) # sample mean
loc # population mean
var(y) # sample variance
2 * b^2 # population variance
## Not run: loc <- 0; b <- 1.5; x <- seq(-5, 5, by = 0.01)
plot(x, dlaplace(x, loc, b), type = "l", col = "blue", ylim = c(0,1),
main = "Blue is density, orange is cumulative distribution function",
sub = "Purple are 5,10,...,95 percentiles", las = 1, ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(qlaplace(seq(0.05,0.95,by = 0.05), loc, b),
dlaplace(qlaplace(seq(0.05, 0.95, by = 0.05), loc, b), loc, b),
col = "purple", lty = 3, type = "h")
lines(x, plaplace(x, loc, b), type = "l", col = "orange")
abline(h = 0, lty = 2)
## End(Not run)
plaplace(qlaplace(seq(0.05, 0.95, by = 0.05), loc, b), loc, b)
``` |

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