Discriminating Between the Logistic and the Normal Distributions based on Likelihood Ratio

by Franšois Aucoin and Fahim Ashkar.

Abstract: The problem of discriminating between the normal and the logistic distributions with unknown parameters and based on the likelihood ratio statistic is considered. The main interest is in determining the probability of correct selection (PCS) between these two distributions. Asymptotic approximations to these PCSĺs are derived and then assessed using Monte Carlo (MC) simulations. The MC simulations suggest the asymptotic approximations to be unreliable for sample sizes below 100. Results also reveal a clear difficulty in discriminating between the two distributions for sample sizes smaller than 50.

Key Words: Likelihood Ratio, Discrimination, Normal and Logistic Distributions, Asymptotic Approximation, Monte Carlo Simulations

Franšois Aucoin, frank.aucoin@gmail.com
Fahim Ashkar, ashkarf@umoncton.ca

Editor: Subrata Chakraborty, subrata_arya@yahoo.co.in

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