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On Dwass' method for deriving the distribution of rank order statistics

B. R. Handa, Sri Gopal Mohanty (1979)

Aplikace matematiky

This note presents a critical examination of Dwass' method for obtaining the distribution of rank order statistics defined on random samples obtained from the same continuous population. New situations are discussed for the usefulness of the method.

On goodness-of-fit for the absence of memory model

Vilijandas Bagdonavičius, Rüta Levulienė (2001)

Kybernetika

Logrank-type and Kolmogorov-type goodness-of-fit tests for the absence of memory model are proposed when the accelerated experiments are done under step-stresses. The power of the test against the approaching alternatives is investigated. The theoretical results are illustrated with simulated data.

On testing hypotheses in the generalized Skillings-Mack random blocks setting

František Rublík (2011)

Kybernetika

The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons...

On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties

František Rublík (2007)

Kybernetika

Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities. A modification...

On the asymptotic properties of rank statistics for the two-sample location and scale problem

Mohamed N. Goria, Dana Vorlíčková (1985)

Aplikace matematiky

The equivalence of the symmetry of density of the distribution of observations and the oddness and evenness of the score-generating functions for the location and the scale problem, respectively, is established at first. Then, it is shown that the linear rank statistics with scores generated by these functions are asymptotically independent under the hypothesis of randomness as well as under contiguous alternatives in the last part of the paper. The linear and quadratic forms of these statistics...

On the computation of the exact distribution of power divergence test statistics

Marco A. Marhuenda, Yolanda Marhuenda, Domingo Morales (2003)

Kybernetika

In this paper we introduce several algorithms to generate all the vectors in the support of a multinomial distribution. Computational studies are carried out to analyze their efficiency with respect to the CPU time and to calculate their efficiency frontiers. The proposed algorithm is used to calculate exact distributions of power divergence test statistics under the hypothesis of uniformity. Finally, several exact power comparisons are done for different divergence statistics and families of alternatives...

On the distributions of R m n + ( j ) and ( D m n + , R m n + ( j ) )

Jagdish Saran, Kanwar Sen (1982)

Aplikace matematiky

The contents of the paper is concerned with the two-sample problem where F m ( x ) and G n ( x ) are two empirical distribution functions. The difference F m ( x ) - G n ( x ) changes only at an x i , i = 1 , 2 , ... , m + n , corresponding to one of the observations. Let R m n + ( j ) denote the subscript i for which F m ( x i ) - G n ( x i ) achieves its maximum value D m n + for the j th time ( j = 1 , 2 , ... ) . The paper deals with the probabilities for R m n + ( j ) and for the vector ( D m n + , R m n + ( j ) ) under H 0 : F = G , thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model.

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