Kullback–Leibler divergence measure based tests concerning the biasness in a sample

In this paper two tests are proposed, based on the Kullback–Leibler divergence measure, for testing hypotheses concerning the existence and the nature of bias in samples. The first is used to test the existence of bias in a sample, while the second test is used to verify the biasness suggested by the sampling mechanism used. We focus on sampling mechanisms for which the probability of a unit to be selected is proportional to a positive quantity w(x)w(x), with E[w(X)]<∞E[w(X)]<∞. Special attention is given to the weight function w(x)=xrw(x)=xr. The tests are developed for complete as well as for type I right censored samples and their properties are presented. The tests are simple in structure and involve the arithmetic, the geometric and the harmonic mean of the sample. Simulation results are presented for the Weibull distribution and both tests are applied on real life data sets.