On length and area-biased Maxwell distributions

This article addresses the various properties and different methods of estimation of the unknown parameter of length and area-biased Maxwell distributions. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of length and area-biased Maxwell distributions (such as moments, moment-generating function (mgf), hazard rate function, mean residual lifetime function, residual lifetime function, reversed residual life function, conditional moments and conditional mgf, stochastic ordering, and measures of uncertainty) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimator, moments estimator, least-square and weighted least-square estimators, maximum product of spacings estimator and compare them using extensive numerical simulations. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using inverted gamma prior for the scale parameter. Furthermore, Bayes estimators and their respective posterior risks are computed and compared using Markov chain Monte Carlo (MCMC) algorithm. Also, bootstrap confidence intervals using frequentist approaches are provided to compare with Bayes credible intervals. Finally, a real dataset has been analyzed for illustrative purposes.     

20世纪初俄国在西藏的阴谋

本文引用了丰富的档案和报刊资料,考述了20世纪初英国远征军入侵西藏前后而发生的种种诡秘事件,其中主要涉及两位俄属布里亚特蒙古人,一位是十三世达赖喇嘛的＂洗礼大师＂阿旺·德尔智,另一位是受雇于俄国外交部曾在俄国参谋部中亚探险与情报工作印度小组受过训的泽仁布,他们的神秘使命在于利用其民族和宗教外衣的掩护,达到如何影响达赖喇嘛与英国抗衡目的,从而使俄国能在西藏问题上保持或扩大自己的影响。     

On the construction of balanced and orthogonal arrays

Two series of three symbol balanced arrays of strength two are constructed. Using special classes of BIB designs, two classes of two symbol orthogonal arrays of strength three are constructed.     

Evaluating new product decision processes

The development of a new product is often a sequential-decision process with many available stages at which the product may take any one of a number of alternate courses of action. This paper identifies an efficient algorithm for solving this sequential-decision process. A computer program, involving the algorithm, has been written to solve problems containing up to one thousand stages. Input into the program includes the subjective probabilities of success for each decision branch, the cost associated with each decision stage and level, the rate for discounting all monetary values to the present plus an indicator for each decision stage and level of the desired decision criterion. The algorithm utilizes the dynamic-programming solution approach. The output of the algorithm contains the minimum, or maximum, expected discounted decision values for each stage and level of the network. The algorithm and computer program have been primarily utilized in the pharmaceutical industry. An illustrative, exemplary use of the algorithm in this industry is presented.     

A new class of multivariate skew distributions with applications to bayesian regression models

Abstract: The authors develop a new class of distributions by introducing skewness in multivariate elliptically symmetric distributions. The class, which is obtained by using transformation and conditioning, contains many standard families including the multivariate skew‐normal and t distributions. The authors obtain analytical forms of the densities and study distributional properties. They give practical applications in Bayesian regression models and results on the existence of the posterior distributions and moments under improper priors for the regression coefficients. They illustrate their methods using practical examples.     

Green supply chain performance measurement using fuzzy ANP-based balanced scorecard: a collaborative decision-making approach

The purpose of this paper is to delineate a green supply chain (GSC) performance measurement framework using an intra-organisational collaborative decision-making (CDM) approach. A fuzzy analytic network process (ANP)-based green-balanced scorecard (GrBSc) has been used within the CDM approach to assist in arriving at a consistent, accurate and timely data flow across all cross-functional areas of a business. A green causal relationship is established and linked to the fuzzy ANP approach. The causal relationship involves organisational commitment, eco-design, GSC process, social performance and sustainable performance constructs. Sub-constructs and sub-sub-constructs are also identified and linked to the causal relationship to form a network. The fuzzy ANP approach suitably handles the vagueness of the linguistics information of the CDM approach. The CDM approach is implemented in a UK-based carpet-manufacturing firm. The performance measurement approach, in addition to the traditional financial performance and accounting measures, aids in firm’s decision-making with regard to the overall organisational goals. The implemented approach assists the firm in identifying further requirements of the collaborative data across the supply-cain and information about customers and markets. Overall, the CDM-based GrBSc approach assists managers in deciding if the suppliers’ performances meet the industry and environment standards with effective human resource.     

Singular weighing designs and estimation of total weight

The problem of estimation of total weight of objects using a singular spring balance weighing design has been studied in this paper. A lower bound of the estimated total weight is obtained and some classes of designs attaining the lower bound are studied.     

Bayesian approach to change point problems

A Bayesian approach is considered to study the change point problems. A hypothesis for testing change versus no change is considered using the notion of predictive distributions. Bayes factors are developed for change versus no change in the exponential families of distributions with conjugate priors. Under vague prior information, both Bayes factors and pseudo Bayes factors are considered. A new result is developed which describes how the overall Bayes factor has a decomposition into Bayes factors at each point. Finally, an example is provided in which the computations are performed using the concept of imaginary observations.     

ON THE POWER BREAKDOWN OF THE NEGATIVE EXPONENTIAL DISPARITY TESTS

The generalized negative exponential disparity, discussed in Bhandari et al. (Robust inference in parametric models using the family of generalized negative exponential disparities, 2006, ANZJS, 48 , 95–114), represents an important class of disparity measures that generates efficient estimators and tests with strong robustness properties. In their paper, however, Bhandari et al. failed to provide a sharp lower bound for the power breakdown point of the corresponding tests. This was acknowledged by the authors, who indicated the possible existence of a sharper bound, but noted that they did not “have a proof at this point”. In this paper we provide an improved bound for this power breakdown point, and show with an example how this can enhance the existing results.