Estimation and comparison of the stress-strength models with more than two states under Weibull distribution and type II censoring scheme

This paper presents the extension of the inferences on the stress-strength reliability in more than two states to the system depending on the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. The main objective of present paper is to consider different method of estimation, under Type II censoring, for the stress-strength models and to compare them, in more than two states, to the system depending on the ratio of the strength and stress values, when the stress and strength follow independent Weibull distributions, sharing the common shape parameter α.     

Second-order approximations for a multivariate analog of Behrens-Fisher problem through three-stage procedure

Abstract

In this article, we have proposed a three-stage procedure for the estimation of the difference of the means of two multivariate normal populations having unknown and unequal variances. Point as well as confidence region estimation is done for the same. Here, we have used the concept of classical Behrens-Fisher problem. Second-order approximations are obtained in both the cases, i.e., point estimation and confidence region estimation.     

UMVU estimation of the reliability function of the generalized life distributions

The problems of estimating the reliability function and P=P_rX > Y are considered for the generalized life distributions. Uniformly minimum variance unbiased estimators (UMVUES) of the powers of the parameter involved in the probabilistic model and the probability density function (pdf) at a specified point are derived. The UMVUE of the pdf is utilized to obtain the UMVUE of the reliability function and ‘P’. Our method of obtaining these estimators is quite simple than the traditional approaches. A theoretical method of studying the behaviour of the hazard-rate is provided.     

A two-stage minimax procedure with screening for selecting the largest normal mean (ii): an improved pcs lower bound and associated tables

This paper is a follow-up to an earlier article by the authors in which they proposed a two-stage procedure with screening to select the normal population with the largest population mean when the populations have a common known variance. The two-stage procedure has the highly desirable property that the expected total number of observations required by the procedure is always less than the total number of observations required by the corresponding single-stage procedure of Bechhofer (1954), regardless of the configuration of the population means. The present paper contains new results which make possible the more efficient implementation of the two-stage procedure. Tables for this purpose are given, and the improvements achieved (which are substantial) are assessed.     

Using Real‐Time Decision Tools to Improve Distributed Decision‐Making Capabilities in High‐Magnitude Crisis Situations*

Multi‐organizational collaborative decision making in high‐magnitude crisis situations requires real‐time information sharing and dynamic modeling for effective response. Information technology (IT) based decision support tools can play a key role in facilitating such effective response. We explore one promising class of decision support tools based on machine learning, known as support vector machines (SVM), which have the capability to dynamically model and analyze decision processes. To examine this capability, we use a case study with a design science approach to evaluate improved decision‐making effectiveness of an SVM algorithm in an agent‐based simulation experimental environment. Testing and evaluation of real‐time decision support tools in simulated environments provides an opportunity to assess their value under various dynamic conditions. Decision making in high‐magnitude crisis situations involves multiple different patterns of behavior, requiring the development, application, and evaluation of different models. Therefore, we employ a multistage linear support vector machine (MLSVM) algorithm that permits partitioning decision maker response into behavioral subsets, which can then individually model and examine their diverse patterns of response behavior. The results of our case study indicate that our MLSVM is clearly superior to both single stage SVMs and traditional approaches such as linear and quadratic discriminant analysis for understanding and predicting behavior. We conclude that machine learning algorithms show promise for quickly assessing response strategy behavior and for providing the capability to share information with decision makers in multi‐organizational collaborative environments, thus supporting more effective decision making in such contexts.     

Unbiased estimation of the MSE matrices of improved estimators in linear regression

Stein-rule and other improved estimators have scarcely been used in empirical work. One major reason is that it is not easy to obtain precision measures for these estimators. In this paper, we derive unbiased estimators for both the mean squared error (MSE) and the scaled MSE matrices of a class of Stein-type estimators. Our derivation provides the basis for measuring the estimators' precision and constructing confidence bands. Comparisons are made between these MSE estimators and the least squares covariance estimator. For illustration, the methodology is applied to data on energy consumption.