A Discussion of Permutation Tests Conditional to Observed Responses in Unreplicated 2 M Full Factorial Designs

ABSTRACT

In this article we present a new solution to test for effects in unreplicated two-level factorial designs. The proposed test statistic, in case the error components are normally distributed, follows an F random variable, though our attention is on its nonparametric permutation version. The proposed procedure does not require any transformation of data such as residualization and it is exact for each effect and distribution-free. Our main aim is to discuss a permutation solution conditional to the original vector of responses. We give two versions of the same nonparametric testing procedure in order to control both the individual error rate and the experiment-wise error rate. A power comparison with Loughin and Noble's test is provided in the case of a unreplicated 2⁴ full factorial design.     

Estimators for the Finite Mixture of Rayleigh Model Based on Progressively Censored Data

In this article, based on progressively Type-II censored samples from a heterogeneous population that can be represented by a finite mixture of two-component Rayleigh lifetime model, the problem of estimating the parameters and some lifetime parameters (reliability and hazard functions) are considered. Both Bayesian and maximum likelihood estimators are of interest. A class of natural conjugate prior densities is considered in the Bayesian setting. The Bayes estimators are obtained using both the symmetric (squared error) loss function, and the asymmetric (LINEX and General Entropy) loss functions. It has been seen that the estimators obtained can be easily evaluated for this type of censoring by using suitable numerical methods. Finally, the performance of the estimates have been compared on the basis of their simulated maximum square error via a Monte Carlo simulation study.     

An Enhanced Double MEWMA Controller for Drifted MIMO Systems

For a drifted multiple-input and multiple-output (MIMO) system, the double multivariate exponentially weighted moving average (dMEWMA) controller is a popular run-to-run (RTR) controller for adjusting the process mean to a desired target. The stability and performance of dMEWMA controller had been widely studied in literature. Although the dMEWMA controller (with suitable discount matrices) can guarantee long-term stability, it usually requires a moderately large number of runs to bring the process output to approach its desired target if the initial recipe is not chosen appropriately. Due to the initial recipe possibly having an infinite number of feasible solutions for MIMO systems, “how to determine an optimal setting for the initial recipe” turns out to be an interesting research topic. In this article, by solving a constrained optimization problem, we first obtain an optimal initial setting for the input recipe. Then, motivated by this setting, we propose an enhanced dMEWMA controller. The long-term stability conditions and short-term performance of the proposed controller are also addressed. Given a fixed and finite production run, it reveals that the proposed controller has the ability of reducing total mean squared error (TMSE) better than the conventional dMEWMA controller.     

Estimation and Prediction for Exponentiated Family of Distributions Based on Records

In this article, a family of distributions, namely the exponentiated family of distributions, is defined and for the unknown parameters, different point estimates are derived based on record statistics. Prediction for future record values is presented from a Bayesian view point. Two numerical examples and a Monte Carlo simulation study are presented to illustrate the results.     

Mathematical forms of the distribution of the product of two normal variables

This paper finds the mathematical forms of the distribution of the product where x and x follow a bivariate normal distribution In this paper the distribution when PT0 is expressed as an integral, a new, fundamental result. From this general form, six different cases can be distinguished depending on what is known about the parameters and p. The special cases are Aroian $year:1959 and (6) Additionally, we prove that if and as the distribution of the product approaches the Type III distribution. When p=0# Aroian $year:1959 and Aroian and Meeker $year:1977, give tables for various values of 6., 6 . The results in this paper will be used to provide brief tables for p^O in a separate paper     

A generalization of mosteller's test

A generalization of Mosteller's test for slippage of the location parameter is proposed. The distribution of the test statistic under the null hypothesis is obtained and the power of the test is compared with that of Mosteller's test     

Comments on the special issue of communications in statistics (vol.a8, no. 10) concerned with weather modification experiments

As stated by the Editors of the Special Issue. It was complied with reference to two of my statements; that much of the current weather modification literature is slanted and unreliable. and(2) that progress in the building of a reliable weather modification technology requires an interdisciplinary study of as many completed cloud seeding experiments as possible. The material published in the Special Issue relates to two completed experiments, the Tasmania and the Israeli experiments. It is shown that a realistic appraisal of a completed experiment requires a prolonged effort, including an examination of quite a few relevant publications and, on occasion, Some numerical work on published raw data. It appears that an interdisciplinary reanalysis of the Tasmania experiment can contribute to the development of a reliable cloud seeding technology.     

Identifiability of distributions under competing risks and complementary risks model

Let X₁,X₂,…,X_p be p random variables with cdf's F₁(x),F₂(x),…,F_p(x)respectively. Let U = min(X₁,X₂,…,X_p) and V = max(X₁,X₂,…,X_p).In this paper we study the problem of uniquely determining and estimating the marginal distributions F₁,F₂,…,F_p given the distribution of U or of V.

First the problem of competing and complementary risks are introduced with examples and the corresponding identification problems are considered when the X₁'s are independently distributed and U(V) is identified, as well as the case when U(V) is not identified. The case when the X₁'s are dependent is considered next. Finally the problem of estimation is considered.     

Errors in inspection and grading distributional aspects ofscreening and merarchal screening

Continuing the studies of Johnson et al (1980) and Johnson and Kotz (1981), further distributions arising from models of errors in inspection and grading of samples from finite, possibly stratified lots are obtained. Screening, and hierarchal screening forms of inspection are also considered, and the effects of errors on the advantages of these techniques assessed.