Fréchet and Inverse Gamma Distributions: Correct Selection and Minimum Sample Size to Discriminate Them

Abstract

In this article, we propose a likelihood ratio test to discriminate between the inverse gamma and Fréchet distributions. The asymptotic distribution of the logarithm of the ratio of the maximized likelihoods under the null hypothesis is provided for both cases; the data come from the Fréchet and inverse gamma models. We also provide the minimum sample size required to discriminate between the two distributions when the probability of correct selection is fixed. A simulation study is presented in order to compare the empirical and asymptotic probabilities of the correct selection. The article is motivated by two applications to real data sets.

AMS Subject Classification:

• 33C90
• 62E99

Keywords:

• Asymptotic distribution
• Fréchet distribution
• Inverse gamma distribution
• Likelihood ratio test
• Probability of correct selection