VGAM: laplaceUC – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

laplaceUC

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.
`p`	vector of probabilities.
`n`	number of observations. Same as in `runif`.
`location`	the location parameter a, which is the mean.
`scale`	the scale parameter b. Must consist of positive values.
`log`	Logical. If `log = TRUE` then the logarithm of the density is returned.
`lower.tail, log.p`	Same meaning as in `pnorm` or `qnorm`.

Details

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.

Value

dlaplace gives the density, plaplace gives the distribution function, qlaplace gives the quantile function, and rlaplace generates random deviates.

Author(s)

T. W. Yee and Kai Huang

References

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

Examples

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)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13