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A New Closed-form Approximation for the Skew Normal Distribution with Applications

Idowu O. Ayodeji


The paper presents a closed-form approximation for skew normal distribution using the (approximate) equivalence link between the normal and the logistic distribution functions. Consequently, the approximation may be used in lieu of the skew normal (SN) distribution to enhance technical simplicity and mathematical tractability. In addition, consistency of the estimators of the parameters of the proposed closed-form was discussed. Finally, synthetic
datasets of selected sample sizes n = 25; 50; 100; 500; 1000 and four sets of real-life data comprising of two economic datasets and two others from copious literature were used to test the adequacy of the proposed specification. The study concluded that the proposed model provided a very good approximation for SN such that can be used in further mathematical derivations involving the skew normal, and also for inclusion in software programs.


normal CDF, logistic distribution, simulation, Otis scores, econometrics.

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