A Bayes comparison of Weibull extension and modified Weibull models for data showing bathtub hazard rate

A number of models have been proposed in the literature to model data reflecting bathtub-shaped hazard rate functions. Mixture distributions provide the obvious choice for modelling such data sets but these contain too many parameters and hamper the accuracy of the inferential procedures particularly when the data are meagre. Recently, a few distributions have been proposed which are simply generalizations of the two-parameter Weibull model and are capable of producing bathtub behaviour of the hazard rate function. The Weibull extension and the modified Weibull models are two such families. This study focuses on comparing these two distributions for data sets exhibiting bathtub shape of the hazard rate. Bayesian tools are preferred due to their wide range of applicability in various nested and non-nested model comparison problems. Real data illustrations are provided so that a particular model can be recommended based on various tools of model comparison discussed in the paper.     

New approximate confidence intervals for the difference between two Poisson means and comparison

The problem of estimating the difference between two Poisson means is considered. A new moment confidence interval (CI), and a fiducial CI for the difference between the means are proposed. The moment CI is simple to compute, and it specializes to the classical Wald CI when the sample sizes are equal. Numerical studies indicate that the moment CI offers improvement over the Wald CI when the sample sizes are different. Exact properties of the CIs based on the moment, fiducial and hybrid methods are evaluated numerically. Our numerical study indicates that the hybrid and fiducial CIs are in general comparable, and the moment CI seems to be the best when the expected total counts from both distributions are two or more. The interval estimation procedures are illustrated using two examples.     

Distance equalizers

Distance equalizers are introduced as empirical measures of central tendency that make distances to univariate data as similar as possible. These measures are made precise by means of various so-called fluctuation functions which account for distances in different ways. Distance equalizers differ from the mean as well as from the median. Also, distance equalizers relate to dispersion measures. Algorithms and closed-form solutions for special cases are given. Some computations require to perform multiextremal function minimization. Distance equalization is extendable to data from higher dimensions and to function quantization in signal processing.     

Book reviews

E. Kofler, G. Menges: Entscheidungen bei unvollständiger Information. Lecture Notes in Economics and Mathematical Systems 136. Springer-Verlag, Berlin-Heidelberg-NewYork 1976, 357 S., DM 31.

B. S. Everitt: The Analysis ot Contingency Tables. Chapman and Han, London 1977, 128 S., £ 3.75.

O. Barndorff-Nielsen: Information and Exponential Families in Statistical Theory. J. Wiley & Sons, Chichester-New York-Brisbane-Toronto 1978, 247 S., £ 13.50; $ 28.50.

W. Gilchrist: Statisticai Forecasting. J. Wiley & Sons, London-New York-Sydney-Toronto 1976, 321 S., £ 9.50; $ 19.00.

J. M. Chambers: Computational Methods for Data Analysis. J. Wiley & Sons, New York Chichester-Brisbane-Toronto 1977, 279 pp., £ 11.30.

A. Hughes, D. Grawoig: Statistics: A Foundation for Analysis. Addison-Wesley Publishing Company, Reading-Menlo-Park London-Don Mills 1971, 525 S., $ 11.50.

K.Krickeberg, H.Ziezold: Stochastiche Methoden. Springer Verlag, Berlin-Heidelberg-New York 1977, 201 S., 13 Abb., DM 28.

Ch. Schneeweiss: Inventory-Production Theory. A Linear Policy Approach. Lecture Notes in Economics and Mathematical Systems 151. Springer Verlag, Berlin-Heidelberg-NewYork 1977, 122 S., 13 Abb., 9 Tab., DM 18.

S. Dworatschek: Grundlagen der Datenverarbeltung, 6., völlig neu bearb. u. erw. Aufl., Walter de Gruyter, Berlin-New York 1977, 538 S., 200 Abb., 212 Üb.Aufg., 59 Fotos, DM 38.

H. E. Steinhagen, S. Fuchs:Objekterkennung. Einführung in die mathematischen Methoden der Zeichenerkennung. VEB Verlag Technik, Berlin 1976, 436 S., 165 Abb., 32 Tab., 49,–.M.

G. Tinhofer: Mathematik für Studlenanfänger, Carl Hanser Verlag, München 1977, 464 S., 191 Abb., DM 38.     

Optimum Critical Value for Pre-Test Estimator

In this paper, methods are proposed in finding the robust design in both Taguchi and Standard setups when a signal factor is present. The robust design is a set of level combinations of control factors so that the effect of controllable noise factors on response is minimum. Both univariate and multivariate methods are used in finding the influential noise factors for the determination of robust designs.     

Regression model with elliptically contoured errors

For the regression model y=X β+ε where the errors follow the elliptically contoured distribution, we consider the least squares, restricted least squares, preliminary test, Stein-type shrinkage and positive-rule shrinkage estimators for the regression parameters, β.

We compare the quadratic risks of the estimators to determine the relative dominance properties of the five estimators.     

Der Sequentieile Quotiententest bei irreduziblen homogenen Markovschen Ketten mit endlichem Zustandsraum

The Sequential Probaility Ratio Test is applied to test two simple hypotheses about the transition probability matrix of an irreducible homogeneous MARKOV chain with finite state space. An analogue (14) of Wald's Fundamental Identity, the Operating Characteristic Function (20-21) and the Average Sample Number (22-23) are given. These statements are generalizations of the MARKOV chain as well as some more conditions about the eigenvalues of the transition probability matrix.     

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