In statistics we often experience combining n-independent tests of simple hypothesis, versus a one-tailed alternative as n approaches infinity. In the present study, we consider combining independent tests in case of conditional normal distribution with probability density function Xjh$N ðch; 1Þ; h 2 ½a; 1Þ; a ! 0 when h 1 ; h 2 ; ::: have a distribution function (DF) F h : Four nonparametric combination procedures (Fisher, logistic, sum of p-values and inverse normal) were compared via the exact Bahadur slope. We concluded that the inverse normal procedure is better than the other procedures.
In this paper we assume that the life time of a test unit follows a log-logistic distribution with known scale parameter. Tables of optimum times of changing stress level for simple step-stress plans under a cumulative exposure model are obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the model parameters at the design stress with respect to the change time.Zusammenfassung: In diesem Aufsatz wird angenommen, dass die Lebensdauer einer Testeinheit einer log-logistischen Verteilung mit bekanntem Skalenparameter genügt. Tabellen für die optimalen Zeitpunkte eines Wechsels des Belastungsniveaus für einfache step-stress Pläne unter einem kumulativen Expositionsmodells erhält man durch Minimieren der asymptotischen Varianz des Maximum Likelihood Schätzers der Modellparameter zur zulässigen Spannung bezüglich der Wechselzeit.
For simple null hypothesis, given any non-parametric combination method which has a monotone increasing acceptance region, there exists a problem for which this method is most powerful against some alternative. Starting from this perspective and recasting each method of combining pvalues as a likelihood ratio test, we present theoretical results for some of the standard combiners which provide guidance about how a powerful combiner might be chosen in practice. In this paper we consider the problem of combining n independent tests as n → ∞ for testing a simple hypothesis in case of extreme value distribution (EV(θ,1)). We study the six free-distribution combination test producers namely; Fisher, logistic, sum of p-values, inverse normal, Tippett’s method and maximum of p-values. Moreover, we studying the behavior of these tests via the exact Bahadur slope. The limits of the ratios of every pair of these slopes are discussed as the parameter θ → 0 and θ → ∞. As θ → 0, the logistic procedure is better than all other methods, followed in decreasing order by the inverse normal, the sum of p-values, Fisher, maximum of p-values and Tippett’s procedure. Whereas, θ → ∞ the logistic and the sum of p-values procedures are equivalent and better than all other methods, followed in decreasing order by Fisher, the inverse normal, maximum of p-values and Tippett’s procedure.
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