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Density function, distribution function, quantiles and random number
generation for the normal Laplace distribution, with parameters
dnl(x, mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu,sigma,alpha,beta))
pnl(q, mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu,sigma,alpha,beta))
qnl(p, mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu,sigma,alpha,beta),
tol = 10^(-5), nInterpol = 100, subdivisions = 100, ...)
rnl(n, mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu,sigma,alpha,beta))
dnl
gives the density function, pnl
gives the
distribution function, qnl
gives the quantile function and
rnl
generates random variates.
Vector of quantiles.
Vector of probabilities.
Number of random variates to be generated.
Location parameter
Scale parameter
Skewness parameter
Shape parameter
Specifying the parameters as a vector of the form
c(mu,sigma,alpha,beta)
.
Specified level of tolerance when checking if parameter beta is equal to 0.
The maximum number of subdivisions used to integrate the density and determine the accuracy of the distribution function calculation.
Number of points used in qnl
for cubic
spline interpolation of the distribution function.
Passes arguments to uniroot
.
David Scott d.scott@auckland.ac.nz, Jason Shicong Fu
Users may either specify the values of the parameters individually or
as a vector. If both forms are specified, then the values specified by
the vector param
will overwrite the other ones.
The density function is
The distribution function is
The function millsR
.
Generation of random observations from the normal Laplace distribution
using rnl
is based on the representation
William J. Reed. (2006) The Normal-Laplace Distribution and Its Relatives. In Advances in Distribution Theory, Order Statistics and Inference, pp. 61--74. Birkhäuser, Boston.
param <- c(0,1,3,2)
par(mfrow = c(1,2))
## Curves of density and distribution
curve(dnl(x, param = param), -5, 5, n = 1000)
title("Density of the Normal Laplace Distribution")
curve(pnl(x, param = param), -5, 5, n = 1000)
title("Distribution Function of the Normal Laplace Distribution")
## Example of density and random numbers
par(mfrow = c(1,1))
param1 <- c(0,1,1,1)
data1 <- rnl(1000, param = param1)
curve(dnl(x, param = param1),
from = -5, to = 5, n = 1000, col = 2)
hist(data1, freq = FALSE, add = TRUE)
title("Density and Histogram")
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