Central Tendency Measurements Estimation for Skew Normal Distributions Using Taylor Series Expansion and Simpson’s Rule

Abstract

This study aims to estimate central tendency measurements, including mode and median of skew normal distributions
using Taylor series expansion and Simpson’s Rule. Skew normal distributions are characterized as continuous, unimodal, and strictly
quasi-concave. Specifically, to compute the mode approximately, the derivative of the sum of the first three terms in the T aylor series
expansion is set to be zero and then the equation is solved to find the unknown and to compute the median, the definite integration of
skew normal distribution is evaluated using Simpson’s Rule. SAS macro programs are developed to verify and assess the accuracy of
these computations under different skewness levels.