Graduate Thesis Or Dissertation
 

Performance of some tests for bivariate independence, interchangeability, and equality of distributions of ratios

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  • The purpose of this thesis is to derive and compare asymptotic performances of certain tests of independence, interchangeability and equality of the distributions of_ratios Y/X for positive variates and Y with joint c.d.f. H(x,y) of particular forms. Three bivariate families, Morgenstern, Plackett, and Moran, are considered which permit marginal c.d.f.'s F(x) and G(y) of specified forms. For testing independence of X and Y, asymptotic locally optimal parametric tests are derived for bivariate gamma and Weibull distributions for each of three families. Locally most powerful nonparametric tests are also derived for each of the three bivariate families, and asymptotic relative efficiency comparisons are made among the various tests of independence. Nonparametric tests for interchangeability of X and Y, based on the Wilcoxon, symmetric squared ranks, and Savage statistics are considered. Asymptotic relative efficiency comparisons of the nonparametric tests are made for scale alternatives in the Morgenstern and Moran bivariate gamma distributions and bivariate log normal distributions. Wilcoxon, symmetric squared ranks, and normal score tests are considered for testing equality of two distributions of ratios Y/X. Asymptotic relative efficiency comparisons of the nonparametric tests are made for scale alternatives in some Morgenstern bivariate gamma distributions. The techniques and results of this study may have application in the analysis of data from rain-making experiments, reliability studies and medical research.
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