Maple script for improving test statistics

Abstract

In this work, we present source code for a program (script) that may be used with the algebraic manipulation software Maple, for generating analytic expressions for Bartlett and Bartlett-type corrections to improve likelihood ratio and score statistics on general two parameter distributions. The script is tested on normal, inverse Gaussian, gamma and Weibull distributions, and the results are compared with those published in earlier works, confirming all of the previously reported expressions. The presented script may be in principle applied for calculating the Bartlett and Bartlett-type corrections for any two parameter distribution under orthogonality of parameters.

Keywords:

• Bartlett corrections
• Bartlett-type corrections
• Likelihood ratio
• Score statistic