Laplace {L1pack} | 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. |
location, scale |
location and scale parameters. Scale must be positive. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
p |
vector of probabilities. |
n |
number of observations. If |
If location
or scale
are not specified, they assume the default
values of 0
and 1
respectively.
The Laplace distribution with location μ and scale φ has density
f(x) = 1/(φ√2) exp(-√2|x - μ|/φ)
dlaplace
, plaplace
, and qlaplace
are respectively the density,
distribution function and quantile function of the Laplace distribution. rlaplace
generates random deviates from the Laplace.
The length of the result is determined by n
for rlaplace
, and is
the maximum of the lengths of the numerical parameters for the other functions.
Felipe Osorio and Tymoteusz Wolodzko
Kotz, S., Kozubowski, T.J., and Podgorski, K. (2001). The Laplace Distributions and Generalizations. Birkhauser, Boston.
Phillips, R.F. (2002). Least absolute deviations estimation via the EM algorithm. Statistics and Computing 12, 281-285.
Distributions for other standard distributions and rmLaplace
for the random generation from the multivariate Laplace distribution.
x <- rlaplace(1000) ## Q-Q plot for Laplace data against true theoretical distribution: qqplot(qlaplace(ppoints(1000)), x, main = "Laplace Q-Q plot", xlab = "Theoretical quantiles", ylab = "Sample quantiles") abline(c(0,1), col = "red", lwd = 2)