laplaceUC {VGAM} | 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) plaplace(q, location=0, scale=1) qlaplace(p, location=0, scale=1) rlaplace(n, location=0, scale=1)
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. |
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.
dlaplace
gives the density,
plaplace
gives the distribution function,
qlaplace
gives the quantile function, and
rlaplace
generates random deviates.
T. W. Yee
Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.
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)