An empirical model to predict arsenic pollution affected life expectancy

A robust, globally implementable and simple empirical model to predict the arsenic pollution affected life expectancy using a stepwise regression was developed. Life expectancy calculated using a life table technique requires crude death rates data that are not available for small administrative units, complex calculations and does not consider socioeconomic parameters. Hence, a model was needed to forecast the impact of arsenic pollution and socioeconomic parameters on life expectancy for locations with limited data availability. A linear multiple regression technique was used to develop an empirical model to predict arsenic pollution affected life expectancy at birth. The model was calibrated using nine arsenic polluted administrative blocks of district Murshidabad, West Bengal, India and tested independently for three other arsenic polluted blocks of the same district. The R ² values for the plot of actual versus predicted life expectancy at birth were 0.98 for calibration, testing and independent validation. The model is complementary to the life table technique and offers a means to assist planning by public health engineers and health policy makers to mitigate arsenic pollution on a community priority basis.     

“The Past in the Present: Mills,Tocqueville and the Necessity of History”

Historical sociology has achieved a reasonable degree of respectability in the discipline, and there is much interesting work being produced. But a pronounced aspect of much of this work is an indifference to the question of the value of studying the past as a way to understanding the present. This article argues that, rather than trying to outdo the historians by producing “better,” more theoretically sophisticated history, sociologists would better advance the case for historical sociology by showing how any particular historical study helps illuminate contemporary concerns. The article draws upon the writings of C. Wright Mills and Alexis de Tocqueville to show not just the need for historical sociology but also as indications of how this might best be done.     

Robustness of tests for directional mean

In this paper we study the robustness of the likelihood ratio, circular mean and circular trimmed mean test functionals in the context of tests of hypotheses regarding the mean direction of circular normal and wrapped normal distributions. We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions. The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.     

Estimating parameters of a selected Pareto population

Let Π₁,…,Π_k be k populations with Π_i being Pareto with unknown scale parameter α_i and known shape parameter β_i;i=1,…,k. Suppose independent random samples (X_i1,…,X_in), i=1,…,k of equal size are drawn from each of k populations and let X_i denote the smallest observation of the ith sample. The population corresponding to the largest X_i is selected. We consider the problem of estimating the scale parameter of the selected population and obtain the uniformly minimum variance unbiased estimator (UMVUE) when the shape parameters are assumed to be equal. An admissible class of linear estimators is derived. Further, a general inadmissibility result for the scale equivariant estimators is proved.     

Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.     

Workforce‐constrained Preventive Maintenance Scheduling Using Evolution Strategies

Heavy equipment overhaul facilities such as aircraft service centers and railroad yards face the challenge of minimizing the makespan for a set of preventive maintenance (PM) tasks, requiring single or multiple skills, within workforce availability constraints. In this paper, we examine the utility of evolution strategies to this problem. Comparison of the computational efforts of evolution strategies with exhaustive enumeration to reach optimal solutions for 60 small problems illustrates the ability of evolution strategies to yield optimal solutions increasingly efficiently with increasing problem size. A set of 852 large‐scale problems was solved using evolution strategies to examine the effects of task‐related problem characteristics, workforce‐related variables, and evolution strategies population size (μ) on CPU time. The results empirically supported practical utility of evolution strategies to solve large‐scale, complex preventive maintenance problems involving single‐ and multiple‐skilled workforce. Finally, comparison of evolution strategies and simulated annealing for the 852 experiments indicated much faster convergence to optimality with evolution strategies.     

SB-robustness of directional mean for circular distributions

In this paper we study the robustness of the directional mean (a.k.a. circular mean) for different families of circular distributions. We show that the directional mean is robust in the sense of finite standardized gross error sensitivity (SB-robust) for the following families: (1) mixture of two circular normal distributions, (2) mixture of wrapped normal and circular normal distributions and (3) mixture of two wrapped normal distributions. We also show that the directional mean is not SB-robust for the family of all circular normal distributions with varying concentration parameter. We define the circular trimmed mean and prove that it is SB-robust for this family. In general the property of SB-robustness of an estimator at a family of probability distributions is dependent on the choice of the dispersion measure. We introduce the concept of equivalent dispersion measures and prove that if an estimator is SB-robust for one dispersion measure then it is SB-robust for all equivalent dispersion measures. Three different dispersion measures for circular distributions are considered and their equivalence studied.