Generalized skew-normal models: properties and inference [Statistics 40 (2006) 495–505]

Abstract

In [H.W. Gómez, H.S. Salinas and H. Bolfarine, Generalized skew-normal models: Properties and inference, Statistics 40(6) (2006), pp. 495–505] introduces a new family of asymmetric distributions that depends on two parameters called, α and β, such as for the particular case β = 0 obtained skew-normal distribution. In this note we give a corrected version for the expression that is used in calculating the moments of such distribution.

1. Introduction

The expression (7) given by Gómez et al. 1, known as d _r , used to calculate the moments of incomplete skew-normal distribution is not valid for r = 1. Then not met for r > 1 because this expression is recursive.

The following is a corrected formula for calculating d _r (α). A recursive formulation for computing the incomplete moments of the skew-normal distribution, namely,

is given by:

The previous result is achieved by integrating the expression

between 0 and ∞.

Acknowledgements

H.W. Gómez is partially supported by Grant FONDECYT 1060727|7070074. Hugo S. Salinas is partially supported by Grant DIUDA 221180.