Description Usage Arguments Details Value References See Also Examples
These functions provide the density, distribution function, quantile
function, and random generation for the univariate, symmetric,
log-Laplace distribution with location parameter location
and
scale parameter scale
.
1 2 3 4 |
x, q |
These are each a vector of quantiles. |
p |
This is a vector of probabilities. |
n |
This is the number of observations, which must be a positive integer that has length 1. |
location |
This is the location parameter mu. |
scale |
This is the scale parameter lambda, which must be positive. |
log |
Logical. If |
Application: Continuous Univariate
Density 1: p(theta) = ((sqrt(2)/lambda)^2 / (2*(sqrt(2)/lambda))) * exp(-(sqrt(2)/lambda)*(theta - mu)), theta >= exp(mu)
Density 2: p(theta) = ((sqrt(2)/lambda)^2 / (2*(sqrt(2)/lambda))) * exp((sqrt(2)/lambda)*(theta - mu)),theta < exp(mu)
Inventor: Pierre-Simon Laplace
Notation 1: theta ~ LL(mu, lambda)
Notation 2: p(theta) = LL(theta | mu, lambda)
Parameter 1: location parameter mu
Parameter 2: scale parameter lambda > 0
Mean: E(theta) =
Variance: var(theta) =
Mode: mode(theta) =
The univariate, symmetric log-Laplace distribution is derived from the Laplace distribution. Multivariate and asymmetric versions also exist.
These functions are similar to those in the VGAM
package.
dllaplace
gives the density,
pllaplace
gives the distribution function,
qllaplace
gives the quantile function, and
rllaplace
generates random deviates.
Kozubowski, T. J. and Podgorski, K. (2003). "Log-Laplace Distributions". International Mathematical Journal, 3, p. 467–495.
dalaplace
,
dallaplace
,
dexp
,
dlaplace
,
dlaplacep
,
dmvl
,
dnorm
,
dnormp
, and
dnormv
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | library(LaplacesDemon)
x <- dllaplace(1,0,1)
x <- pllaplace(1,0,1)
x <- qllaplace(0.5,0,1)
x <- rllaplace(100,0,1)
#Plot Probability Functions
x <- seq(from=0.1, to=20, by=0.1)
plot(x, dllaplace(x,0,0.1), ylim=c(0,1), type="l", main="Probability Function",
ylab="density", col="red")
lines(x, dllaplace(x,0,0.5), type="l", col="green")
lines(x, dllaplace(x,0,1.5), type="l", col="blue")
legend(2, 0.9, expression(paste(mu==0, ", ", lambda==0.1),
paste(mu==0, ", ", lambda==0.5), paste(mu==0, ", ", lambda==1.5)),
lty=c(1,1,1), col=c("red","green","blue"))
|
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