Estimating Average Worth of the Selected Subset from Two-Parameter Exponential Populations

ABSTRACT

Suppose independent random samples are available from k(k ≥ 2) exponential populations ∏₁,…,∏ _k with a common location θ and scale parameters σ₁,…,σ _k , respectively. Let X _i and Y _i denote the minimum and the mean, respectively, of the ith sample, and further let X = min{X ₁,…, X _k } and T _i  = Y _i  ? X; i = 1,…, k. For selecting a nonempty subset of {∏₁,…,∏ _k } containing the best population (the one associated with max{σ₁,…,σ _k }), we use the decision rule which selects ∏ _i if T _i  ≥ c max{T ₁,…,T _k }, i = 1,…, k. Here 0 < c ≤ 1 is chosen so that the probability of including the best population in the selected subset is at least P* (1/k ≤ P* < 1), a pre-assigned level. The problem is to estimate the average worth W of the selected subset, the arithmetic average of means of selected populations. In this article, we derive the uniformly minimum variance unbiased estimator (UMVUE) of W. The bias and risk function of the UMVUE are compared numerically with those of analogs of the best affine equivariant estimator (BAEE) and the maximum likelihood estimator (MLE).     

On the coase theorem and coalitional stability: the principle of equal relative concession

The Coase theorem is argued to be incompatible with bargaining set stability due to a tension between the grand coalition and sub-coalitions. We provide a counter-intuitive argument to demonstrate that the Coase theorem may be in complete consonance with bargaining set stability. We establish that an uncertainty concerning the formation of sub-coalitions will explain such compatibility: each agent fears that others may `gang up' against him and this fear forces the agents to negotiate. The grand coalition emerges from the negotiations if each agent uses the principle of equal relative sacrifice to determine the actual allocation. We also establish the rational basis for the choice of the principle of equal relative concession by the negotiating agents. Hence we argue that the Coase theorem will be valid even if there are stable sub-coalitions.     

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.     

A Wavelet‐Based Approach to Preserve Privacy for Classification Mining*

Despite the commercial success of data mining, a major drawback has been acknowledged across academic, industry, and government sectors, namely, the issue of violating the privacy of individuals. We propose a data transformation method based on wavelets to disguise private data while preserving the original classification patterns. Wavelet transformations have been used extensively in signal processing for data reduction, multiresolution analysis, and removing noise from data. In our implementation, two commonly used wavelet transforms, the Haar and the Daub‐4 transforms, are tested for pattern and privacy preservation in classification mining tasks. Empirical results confirm that the Haar and the Daub‐4 transforms preserve the classification patterns and preserve the privacy for real valued data.     

Estimating the parameter of selected uniform population under the squared log error loss function

Let π₁, …, π_k be k (? 2) independent populations, where π_i denotes the uniform distribution over the interval (0, θ_i) and θ_i > 0 (i = 1, …, k) is an unknown scale parameter. The population associated with the largest scale parameter is called the best population. For selecting the best population, We use a selection rule based on the natural estimators of θ_i, i = 1, …, k, for the case of unequal sample sizes. Consider the problem of estimating the scale parameter θ_L of the selected uniform population when sample sizes are unequal and the loss is measured by the squared log error (SLE) loss function. We derive the uniformly minimum risk unbiased (UMRU) estimator of θ_L under the SLE loss function and two natural estimators of θ_L are also studied. For k = 2, we derive a sufficient condition for inadmissibility of an estimator of θ_L. Using these condition, we conclude that the UMRU estimator and natural estimator are inadmissible. Finally, the risk functions of various competing estimators of θ_L are compared through simulation.     

Effect of low back pain on social and professional life of drivers of Kolkata

Abstract Occupational driving has often been associated with a high prevalence of back pain. Buses constitute the backbone of the local transportation; so many people are engaged in the profession. The present study was to investigate the prevalence of low back pain (LBP) and due to that problem whether their social and professional life hampers or not. The present study was undertaken among 160 government undertaking male bus drivers. Modified Nordic musculoskeletal questionnaire was performed with physical assessment. Then Oswestry Low Back Pain Disability Questionnaire (QLBPDQ) was performed to evaluate the extent to which social and professional life is restricted by back pain. Afterwards, the sit-and-reach test and investigation of sitting postures was done. From the analysis of questionnaire it was revealed that drivers had to spend 8-10 hours daily for 6 days in a shift. It was further observed that all of them mainly suffering from LBP. From the QLBPDQ analysis it was found that LBP restricted their social and professional life. Sit and reach test and posture analysis also support this finding. This result is an absolute reflection of the alarming situations of the Kolkata bus drivers. It can be concluded that the bus drivers are highly stressed due to the hazardous working conditions, which in turn may additionally affects their health and overall work performance in the long run.     

An ergonomic study on the onset of mental fatigue among the load handling workers of a central market area in Kolkata

It is a well recognized fact that manual material handling (MMH) entails enormous physical labor and associated discomfort feeling, which invariably culminate into musculoskeletal disorders. However mental fatigue, in such instances, becomes an unexplored parameter that needs definite attention during assessment of work status of MMH workers. The present study is being performed among 75 porters of a central market in Kolkata to ascertain the extent of physical and mental exhaustion among them. SF-12 health status questionnaire followed by another questionnaire involving psychosocial questions were performed among them. The analysis of both the questionnaires clearly revealed that most of the porters are under severe physical exertion as they alone carry about 120 kg load at a time and such activity is repeated at least 40 times throughout the day. They always suffer from pain and discomfort feeling at different body parts and this interferes with their normal work activity to a great extent. Moreover absenteeism means no financial return and even a day's rigourous work fetches meagre income. The inability to support family convincingly even after performing such hazardous tasks makes them feel low. Monotony, boredom, fatigue and mental trauma form an integral part of their daily work schedule.     

Subsidy policies with capital accumulation: Maintaining employment levels

We study a dual economy model of growth and unemployment in the presence of Harris-Todaro type labor migration. The model is a discrete time model of economic growth with given population but endogenous migration of labor. The economy tries to reach development in the quickest possible time while not allowing unemployment to rise above a socially acceptable level. We characterize situations under which maximizing the accumulation of capital in each period is optimal. We also study how particular taxes and subsidies affect unemployment and capital accumulation. Finally, we show that a higher initial capital stock does not necessarily mean a quicker attainment of self-sustained full employment.