A consistent statistical test based on bivariate random samples

Abstract

We propose a consistent test for testing the distribution of bivariate random samples. The probability of type I, type II errors and probability of making no decisions under null and alternative hypotheses are obtained based on copula functions. The consistency of the proposed test is discussed under some null and alternative hypotheses. An unbiased, consistent estimator is proposed for probability of making no decision. Moreover, a simulation study is performed for showing the consistency of the proposed test for some well-known copulas such as independent, Clayton, Gumbel, Frank and Farlie-Gumbel-Morgenstern.