sn (version 0.30)

msn.moment.fit: Fitting multivariate skew-normal distributions with method of moments

Description

Fits a multivariate skew-normal (MSN) distribution to data using the method of moments.

Usage

msn.moment.fit(y)

Arguments

y

a matrix or a vector. If y is a matrix, its rows refer to observations, and its columns to components of the multivariate distribution. If y is a vector, it is converted to a one-column matrix, and a scalar skew-normal distribut

Value

• 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.

Background

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).

Details

This function is used by msn.mle to obtain preliminary estimates, if starting values are not provided. 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.

References

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715--726.

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

See Also

msn.mle, sn.mle