A new formula for the computation of multivariate factorized moments by using the joint cumulative distribution function

This work presents a closed formula to compute any muitivariate factorized expected value from the knowledge of the joint cumulative distribution function (cdf) of any random variable. Additionally, a new nonparametric estimator alternative to the sample average is presented for the univariate case.     

Incomplete moments of modified power series districutions with applications

The recurrence relations between the incomplete moments and the factorial incomplete moments of the modified power series distributions (MPSD) are derived. These relations are employed to obtain the experessions for the incomplete moments and the incomplete factorial moments of some particular members of the MPSD class such as the generalized negative binomial, the generalized Poisson, the generalized logrithmic series, the lost game distribution and the distribution of the number of customers served in a busy period. An application of the incomplete moments of the generalized Poisson distribution is provided in the economic selection of a manufactured product. A numerical example is provided using the Poisson distribution and the Generalized Poisson distribution. The example illustrates the difference in results using the two models     

On a gmanova model likelihood ratio test criterion

For the generalized MANOVA (GMANOVA) model of Potthoff and Roy (1964), X = BξA + E, Khatri (1966) derives the likelihood ratio test criterion for test-ing the composite double linear null hypothesis CξV = 0, C,V known. This criterion plays an important role in statistics, and several authors have recently studied its further properties. However, Khatri's (1966) de-reviation of the distribution of this criterion is involved. By noting that the GMANOVA model is re-stricted MANOVA model, this paper presents an alter-native simple derivation of the distribution of this criterion. The derivation is based on the generalized Sverdrup's lemma, Kabe (1965).     

Generalizations of barlett's and hartley's tests of homogeneity using “overall variability”

The generalized variance plays on important and useful role as a measure to compare overall variability of different populations in biological sciences (Goodman, 1968; Kocherlakota and Kocherlakota, 1983; Sokai, 1965). Here we present simple and elegant multivariate analogues to Bartlett's and Hartley's tests of homogeneity. Large sample distributions of the statistics are presented and the practical usefulness of the tests are demonstrated throught several examples.     

Prediction intervals for the random intercept linear model

Our main purpose is to give a method of constructing prediction intervals for the mean of us future observations in the random intercept linear model, A method is also indicated for constructing exact confidence intervals on the expected value of a future observation.     

On the unbiasedness of iterated gls estimators

We Formulate sufficienct conditions for the existonce of the expectation of iterated generalized expectation of the iterated generalized least squares estimator, which consequently guarantee its unbiasedness, The analysis is applied to the maximum likelihood estimator in the general linear model with normal disturbances, where a set of assumptions ensures convergence of the iteration as well as unbiasedness.     

Estimation of p{x > y} based on progressively truncated versions of the wilcqxon-mann-whitney statistics

Stochastic processes related to some generalized U-statistics (with especial emphasis on the Wilcoxon-Mann-Whitney (WMW-) statistic), under progressive right censoring, are considered for prediction purposes. Their weak convergence results are incorporated in the study of the asymptotic properties of the predictors. The form of the estimable parameter as a function of the truncation point is studied for the WMW case for some typical distributions and the theoretical results are supplemented by simulated ones.     

An efficient procedure for computing minque of variance components and generalized least squares estimates of fixed effects

An efficient method for computing minimum norm quadratic unbiased estimates (MINQUE) of variance components and generalized least squares estimates of the fixed effects in the mixed model is developed. The computing algorithm uses a modification of the W transformation.     

Mixture formulations of a bivariate negative binomial distribution with applications

This paper considers further mixture formulations of the bivariate negative binomial (BNB) distribution of Edwards and Gurland (1961) and Subrahmaniam (1966). These formulations and some known ones are applied (1) to obtain a bivariate generalized negative binomial (BGNB) distribution of Bhattacharya (1966), (2) to establish a connection between the accident-proneness models given by the BNB, BGNB and Bhattacharya's bivariate distributions, and (3) to compute the grade correlation and distribution function of the Wicksell-Kibble bivariate gamma distribution.     

A note on generalized ridge estimators

It is shown that a necessary and sufficient condition derived by Farebrother (1984)for a generalized ridge estimator to dominate the ordinary least-squares estimator with respect to the mean-square-error-matrix criterion in the linear regression model admits a similar interpretation as the well known criterion of Toro-Viz-carrondo and Wallace (1968)for the dominance of a restricted least-squares estimator over the ordinary least-squares estimator. Two other properties of the generalized ridge estimators, referring to the concept of admissibility, are also pointed out.