On the type-B integral equation and the distribution of wilks statist for testing independence of several groups of variables

In this paper, WILKS'type-B integral equation is solved in the general form of a series of beta functions and a series of weighted gamma functions as proposed by WALD and BROOKNER 1941. The coefficients in both representations can be obtained by explicit recurrence relartions, therefore the results solve many distributional problems and have the fewest computational difficulties of any representation that has surfaced to date. The radius of convergence of the second series representation is given, whereas the convergence property of the first series representation is given, whereas the convergence property of the first series representation was studied by WALD and Brookner. The exact null distributions of WILKS' statistic A for testing the independence of several groups of variables and of V = -log A are given. The coefficients in all the series representration can be computed recursilvely and hence can be obtained easily with the help of modern computatinal facilities     

The rank distribution of the maximin in a random matrix

Let S be a set of tm distinct real numbers and R a random t × m matrix of these tm numbers with rows {r_i} and columns (c_i}. Define b = Max Min x. l≤i≤t x?r_i. Let c be the event Max Min x = Min Max x. l≤i≤t x?r_i l≤i≤m x?c_i. This paper derives the probability distribution of the rank of b in S, as well as the same distribution conditional on c.     

Moments of the function of non-normal random vector with applications to econometric estimators and test statistics 1

In this paper we have provided a general result on the moments of a function of nonnormal random vector. The results for the normal case follow as a special case of this result. It is also indicated that the moments of a large class of econometric estimators and test statistics can be obtained by using our general result. This includes least squares estimator in the dynamic model, unit root tests, and the two step semiparametric estimators, among others.     

The Planning Stage in Statistical Reasoning

An important step in the statistical problem-solving process is the selection of the appropriate statistical procedure for the real-world situation under analysis. A decision-tree term project has been found to be an effective teaching device to help MBA students understand this step. The project requires the students to construct a decision-tree structure, which, through a series of questions and responses, will lead from the statement of a statistical question to the appropriate sampling distribution to use in addressing the question.     

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.     

An Adaptive Test for the Two-Sample Location Problem Based on U-Statistics

For the two-sample location problem with continuous data we consider a general class of tests, all members of it are based on U-statistics. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen U-statistics. It is shown that the proposed adaptive test has good asymptotic and finite sample power properties.     

On a preliminary test estimator for one of the parameters of the log-zero-poisson distribution

A discrete distribution called the log-zero-Poisson distribution has been recommended by Katti (c.f. Biometrics 1970) as an alternate to the negative binomial and other distributions usually called "contagious" distributions.A major problem in the use of this and all other contagious distributions has been the difficulty of obtaining the maximum likelihood esti-mates. A custom-made ad hoc estimator, λ, has been proposed for the parameter λ of this distribution in Katti and Khedr (1980). In this paper, its efficiency relative to Fisher information is studied, only to discover that λ can be 30 times better than the maximum likelihood estimate in some parts of the parameter space and much weaker in other parts.A preliminary test is recommended to choose between the estimates, and the efficiency of the procedure is tabulated. As it is to be expected, the resultant estimator equals the better of the two estimators with some error at the values of the parameters where the two estimators are equivalent.