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Approximate skew normal distribution

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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.