Linear and Nonlinear Approximations of the Ratio of the Standard Normal Density and Distribution Functions for the Estimation of the Skew NormalShape Parameter

摘要

We introduce a linear approximation and a nonlinear approximation of the ratio of the standard normal density and distribution functions in presence of an unknown constant representing the shape parameter of the skew normal distribution. The purpose of these approximations is to estimate the skew normal shape parameter. We present a new estimation method of the shape parameter based on these approximations. The simulation results demonstrate that the approximations strongly resemble their true valuesin the regions of interest and the estimated biases of the shape parameter are small.