Discrimination Between Two Inverted Distributions

Source abstract

Two popular life testing models, namely Rayleigh distribution, Half Logistic distributions are considered. The inverted versions of these two distributions are worked out. The graphs of the frequency curves for these distributions on the same scale look identical, which drives to the motivation of testing whether one distribution can be used as an alternative to the other. Between these two distributions Inverse Rayleigh Distribution (IRD) appears in literature earlier than Inverse Half Logistic Distribution (IHLD). The authors have proposed to test IHLD as an alternative model to IRD. In statistical testing of hypothesis, they consider IRD as a null population and IHLD an alternative population and proposed a Likelihood Ratio test procedure to test this hypothesis. The critical values of the test statistic, the power of the test procedure are computed in order to assess the validity of the hypotheses.