Description Usage Arguments Details Value Author(s) References Examples
Functions to calculate the mean, variance, skewness and kurtosis of a specified normal Laplace distribution.
1 2 3 4 5 6 7 8 | nlMean(mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu, sigma, alpha, beta))
nlVar(mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu, sigma, alpha, beta))
nlSkew(mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu, sigma, alpha, beta))
nlKurt(mu = 0, sigma = 1, alpha = 1, beta = 1,
param = c(mu, sigma, alpha, beta))
|
mu |
Location parameter mu, default is 0. |
sigma |
Scale parameter sigma, default is 1. |
alpha |
Skewness parameter alpha, default is 1. |
beta |
Shape parameter beta, default is 1. |
param |
Specifying the parameters as a vector of the form |
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 mean function is
E(Y) = mu + 1/alpha - 1/beta.
The variance function is
var(Y) = sigma^2 + 1/sigma^2 + 1/beta^2.
The skewness function is
skewness = [2/alpha^3 - 2/beta^3]/[sigma^2 + 1/alpha^2 + 1/beta^2]^3/2.
The kurtosis function is
kurtosis = [6/alpha^4 + 6/beta^4]/[sigma^2 + 1/alpha^2 + 1/beta^2]^2.
nlMean
gives the mean of the skew hyperbolic nlVar
the
variance, nlSkew
the skewness, and nlKurt
the kurtosis.
David Scott d.scott@auckland.ac.nz, Jason Shicong Fu
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.
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