Fréchet and Inverse Gamma Distributions: Correct Selection and Minimum Sample Size to Discriminate Them
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.
KeywordsAsymptotic distribution Fréchet distribution Inverse gamma distribution Likelihood ratio test Probability of correct selection
AMS Subject Classification33C90 62E99
Unable to display preview. Download preview PDF.
- Acar, E., K. Agarwal, and S. R. Nassif, 2006. Characterization of total chip leakage using inverse (reciprocal) gamma distribution. IEEE ISCAS, 3029–3032.Google Scholar
- Cox, D. R. 1961. Tests of separate families of hypotheses. Proc. Fourth Berkeley Symposium in Mathematical Statistics and Probability, 105–123. Berkeley, CA: University of California Press.Google Scholar
- Mangasarian, O. L., and W. H. Wolberg. 1990 Cancer diagnosis via linear programming. SIAM News, 23, 1–18.Google Scholar
- Wiens, B. L. 1999. When log-normal and gamma models give different results: A case study. Am. Stat., 53, 89–93.Google Scholar