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).     

Sacrificing Women: A Study of Ritualized Practices among Women Volunteers in India

This study addresses issues related to inequality formation and reproduction, especially in regard to gender dynamics operating in a non-western society. Grounded in a post-colonial understanding of urban educated upper and middle class women NGO volunteers in contemporary India, it analyzes how they negotiate new approaches to challenge existing traditional gender roles, yet in critical ways contribute to their reproduction, particularly the traditional concept of ideal Indian womanhood. Employing structural ritualization theory we examine how ritualized symbolic practices related to the traditional concepts of caretaking, sacrifice, and the concept of natural sexual differences continue to be emphasized in a generation confronted with conflicting expectations about modern women’s roles. Twenty-one testimonies provide the major source of evidence along with data gathered through participant observation. This research enhances our understanding of the power of rituals and how they can continue to shape the cognitions and activities of actors.

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 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.     

Determinants of Individual Giving Behavior in Urban India

This paper, based on a primary sample survey over 1925 earning individuals in the cities of Kolkata, Cuttack and Bengaluru, examines how the individual and household characteristics influence the acts of giving in urban India. The regression results indicate income, family size and property ownership affecting likelihood and extent of giving. Likelihood to give is more with females, though males tend to donate more. There exists threshold income beyond which likelihood to donate is less. Characteristics like age, education, dependency ratio and marital status influence certain acts of giving. As the opportunity cost of non-cash giving increases with the rise in income, cash donations substitute non-cash giving. There also prevails complementarity in the acts of giving. On behavioral front, in addition to work–life balance and pledging, the notion of rational choice seems to be gaining ground.

     

Supplemental Retirement Savings Plans in the Public Sector: Participation and Contribution Decisions by School Personnel

Virtually all full-time state and local government employees are covered by a retirement plan, typically a defined benefit plan, in which they are required to participate. In addition, most school employees have the option of choosing to contribute to a voluntary retirement savings plan offered by their school district. Relative to private sector workers, public employees face an expanded choice of retirement savings plans. Federal tax policies allow state and local governments the opportunity to offer both 401(k) plans and 457 plans to their employees. In addition to these plans, public schools and certain other organizations can offer 403(b) plans to their employees. This paper examines the decision to participate in a voluntary savings plan and the level of contributions for those that enroll in at least one of the plans. The analysis begins by describing the savings options available to public school employees and how these plans differ. The findings indicate that the same economic and demographic factors that influence saving decisions by private workers also drive the decisions of school employees. The three savings plans offered to public employees have many similar characteristics; however, several differences in the plans imply that certain workers may prefer one plan type over the others. Probit and Tobit models of participation in any plan and total annual contributions are estimated. Finally, we estimate the determinants of the decision to choose any one or a combination of savings plans.     

On Testing Exponentiality against NBAFR Alternatives

In this article, we propose an interesting approach for testing exponentiality against NBAFR alternatives. A measure of deviation from exponentiality has been derived on the basis of an inequality which we have proved. A test statistic has been constructed using density estimators and its asymptotic normality established. The consistency of the said test is also proved.     

The plutocratic bias in the Indian consumer price index

Studies have found a plutocratic bias in the traditional Laspeyres‐type consumer price index (CPI), attaching greater importance to expenditure by rich households compared to the poor, while the democratic CPI attaches equal weight to all. The authors calculate the democratic index and estimate the plutocratic bias for the new Indian CPI (launched in 2012), the rural and urban CPIs, and the CPIs of three Indian states from 2012 to 2015. They further develop democratic indices for commodity groups and separate indices for three expenditure brackets. The biases found against less developed states and the poorer sections of the population have important implications for monetary policy and indexation of transfer payments.     

Le biais ploutocratique de l'indice des prix à la consommation indien

Des études montrent que les indices des prix à la consommation (IPC) de type Laspeyres, plutôt calqués sur la structure des dépenses des ménages aisés, souffrent d'un biais ploutocratique. Les auteurs recherchent ce biais en Inde de 2012 à 2015, en construisant un indice démocratique qui met tous les ménages sur un pied d'égalité. Ils analysent la situation pour plusieurs sous‐indices (rural, urbain, régionaux), différentes fonctions de consommation et trois tranches de dépenses. Ils soulignent que le biais mis en évidence, qui pénalise les ménages et régions les plus pauvres, a des répercussions potentielles sur la politique monétaire et l'indexation des paiements de transfert.