tailieunhanh - Approximate skew normal distribution

We propose a new approximate skew normal distribution, it is easy to calculate, convenient, mathematically tractable and is in a closed form. It is particularly useful when the probability density function occurs in an expression to be used for further mathematical derivation or in programs for the skew normal distribution. Also, we propose approximate first moment second moment and variance to the skew normal distribution. A numerical comparison between exact and approximate values of pdf and cdf of the skew normal distribution is carried out. | Journal of Advanced Research 2010 1 341-350 Cairo University Journal of Advanced Research ORIGINAL ARTICLE Approximate skew normal distribution Samir K. Ashour Mahmood A. Abdel-hameed Department of Mathematics Institute of Statistical Studies and Research Cairo University Egypt Received 23 December 2009 revised 16 February 2010 accepted 3 March 2010 Available online 24 July 2010 KEYWORDS Skew normal distribution Skewness Approximation Cumulative distribution function Abstract We propose a new approximate skew normal distribution it is easy to calculate convenient mathematically tractable and is in a closed form. It is particularly useful when the probability density function occurs in an expression to be used for further mathematical derivation or in programs for the skew normal distribution. Also we propose approximate first moment second moment and variance to the skew normal distribution. A numerical comparison between exact and approximate values of pdf and cdf of the skew normal distribution is carried out. 2010 Cairo University. Production and hosting by Elsevier . All rights reserved. Introduction Azzalini 1 defined the skew-normal distribution for a random variable Z with the parameter k be g z 2 z U kz 1 z 1 k 2 R where and df are the standard normal density and distribution function respectively density function can be expressed in the following form Corresponding author. Tel. 202 25167483 fax 202 37482533. E-mail address ashoursamir@ . Ashour . 2090-1232 2010 Cairo University. Production and hosting by Elsevier . All rights reserved. Peer review under responsibility of Cairo University. doi Production and hosting by Elsevier 1 kz 1 g z 2 pU ex -z2 2 expCt2 2 dt v2p 1 V 2p for any given k 2 R and 1 z 1. The term skew normal SN refers to a parametric class of probability distributions that extend the normal distribution by an additional shape parameter that regulates the skewness allowing for a .