msn.moment.fit {sn} | R Documentation |
Fits a multivariate skew-normal (MSN) distribution to data using the method of moments
msn.moment.fit(y)
y |
a matrix or a vector. In y is a matrix, its rows refer to
observations, and its columns to components of the multivariate
distribution. In y is a vector, it is converted to a one-column
matrix, and a scalar skew-normal distribution is fitted.
|
This function is used by msn.mle
to obtain preliminary
estimates if it is not provided starting values. After removing
the regression component, estimated by ordinary least squares,
msn.moment.fit
is used to obtain preliminary estimate of
the other parameters from the least squares residuals.
Although the function accepts a vector y
as input, the use of
sn.mle
is recommended in the scalar case.
a list containing the following components:
xi |
a vector with the location parameter |
Omega |
a variance matrix representing the association parameter |
alpha |
a vector of shape parameters |
omega |
vector of scale parameters corresponding to Omega
|
delta |
the parameter delta which determines the shape of the marginal
distributions
|
skewness |
numeric vector with marginal indices of skewness (the standardised third cumulant) |
admissible |
a logical value indicating if the estimated parameters lie in the admissible region |
The multivariate skew-normal distribution is discussed by
Azzalini and Dalla Valle (1996); the (Omega,alpha)
parametrization
adopted here is the one of Azzalini and Capitanio (1999).
Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715726.
Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579602.