laplaceUC {VGAM}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)
plaplace(q, location=0, scale=1)
qlaplace(p, location=0, scale=1)
rlaplace(n, location=0, scale=1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. Positive integer of length 1.
location the location parameter mu, which is the mean.
scale the scale parameter b. Must consist of positive values.

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-mu|/b )

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

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

References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

Examples

loc = 1; b = 2
y = rlaplace(n=100, loc=loc, scale=b)
mean(y)
loc      # population mean
var(y)
2 * b^2  # population variance

## Not run: 
x = seq(-5, 5, by=0.01)
loc = 0; b = 1.5
plot(x, dlaplace(x, loc, b), type="l", col="blue", ylim=c(0,1),
     main="Blue is density, red 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="red")
abline(h=0, lty=2)
## End(Not run)

plaplace(qlaplace(seq(0.05,0.95,by=0.05), loc, b), loc, b)

[Package VGAM version 0.7-1 Index]