laplaceUC | R Documentation |

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

and scale parameter `scale`

.

```
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)
```

`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) = \frac{1}{2b} \exp \left( - \frac{|y-a|}{b}
\right)
```

where `-\infty<y<\infty`

,
`-\infty<a<\infty`

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.

`laplace`

.

```
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",
main = "Blue is density, orange is the CDF", ylim = c(0,1),
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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