Stochastic Comparisons Of The Largest Order Statistics And Discriminant Analysis

As a useful tool, stochastic comparison is very useful in applied probability, statis-tics, reliability, actuary science, and other fields, and stochastic orders also play very important role. This dissertation focus on stochastic comparisons of the maxima in two geometric samples and exponential model with a resilience parameter, and discrimi-nating between the Beta distribution and Kumaraswamy distribution. The optimal allocation of redundancy in consecutive k-out-of-n systems are also studied.First, we study some stochastic comparisons of the maxima in two multiple-outlier geometric samples based on the likelihood ratio order, hazard rate order and usual stochastic order. We establish a sufficient condition on parameter vectors for the likelihood ratio ordering to hold. For the special case when n=2, it is proved that the p-larger order between the two parameter vectors is equivalent to the hazard rate order as well as usual stochastic order between the two maxima.Second, we studies the likelihood ratio order, the hazard rate order and the usual stochastic order of the maximum in two multiple-outlier exponential sample with a resilience parameter. Also, the likelihood ratio order is built for the maximum of sample with proportional reversed hazard rates.Third, we use the ratio of the maximized likelihoods in choosing between a beta distribution and a kumaraswamy distribution. We obtain asymptotic distributions of the logarithm of the ratio of the maximized likelihoods under null hypotheses. We perform some numerical experiments to observe how the methods work for different sample sizes. It is observed that the results work quite well even for small samples limit.Finally, we consider the problems of optimal allocation of a consecutive k-out-of-n systems with respect to the usual stochastic order.