On a class exhibiting trend change in average failure rate

Abstract

Weak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984 Loh, W. Y. 1984. A new generalization of the class of NBU distributions. IEEE Transactions on Reliability R-33 :97–113[Crossref], [Web of Science ®] , [Google Scholar])). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class.     

The status of women among the scheduled tribes in India

The scheduled tribes constitute about 8.2% of the total population in India. Although there is a large volume of anthropological literature describing the characteristics of and differences among the various tribes in India, little inter-disciplinary research has been done to uncover the status of women among the tribal population in India. This paper will analyze the status of women among the scheduled tribes in India. Frequent comparisons will be made to the social and cultural practices of the scheduled tribes, mainstream Hindus, as well as the scheduled caste population. Through this analysis, we will show the distinctiveness of the tribal cultures and the fact that many women from the scheduled tribes face less discrimination than Hindu women and those from scheduled castes.     

Long term demographic effect of a constant stream of immigration when the population is not reproducing itself

The author describes the use of a model to investigate "the age composition of the stationary population resulting from a condition of below replacement fertility and a continuous stream of immigrants, the size of which for any age remain invariant over time.... We have shown that the number dying among [migrants] is the same as the number of them entering over any time interval, and that is precisely how their stationarity is maintained." The geographical focus is on developed countries that are experiencing below-replacement fertility levels. (SUMMARY IN FRE AND SPA)     

BERTRAND COMPETITION WITH ASYMMETRIC MARGINAL COSTS

This article tests the prediction of three discrete asymmetric duopoly price competition games in the laboratory. The games differ from each other in terms of the size of the cost asymmetry that induces a systematic variation in the difference between the firms' marginal costs. While the standard theory requires the low‐cost firm to set a price just equal to the high‐cost firm's marginal cost, which is identical across all three games, and win the entire market, intuition suggests that market price may increase with a decrease in the absolute difference between the two marginal costs. We develop a quantal response equilibrium model to test our competing conjecture. (JEL L11, L12, C91, D43)     

Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

Measurement error in regression analysis

Consider the linear regression model Y = Xθ+ ε where Y denotes a vector of n observations on the dependent variable, X is a known matrix, θ is a vector of parameters to be estimated and e is a random vector of uncorrelated errors. If X'X is nearly singular, that is if the smallest characteristic root of X'X s small then a small perurbation in the elements of X, such as due to measurement errors, induces considerable variation in the least squares estimate of θ. In this paper we examine for the asymptotic case when n is large the effect of perturbation with regard to the bias and mean squared error of the estimate.     

Implementing a Multidimensional Poverty Measure Using Mixed Methods and a Participatory Framework

Recently, there have been advances in the development of multidimensional poverty measures. Work is needed however on how to implement such measures. This paper deals with the process of selecting dimensions and setting weights in multidimensional poverty measurement using qualitative and quantitative methods in a participatory framework. We estimate the multidimensional poverty measures developed by Alkire and Foster for a particular group: persons with psychiatric diagnoses in the United States. To select relevant dimensions and their relative ordering, two discussion groups are convened: one consisting of persons with lived-experience expertise and the other consisting of people with mental health service provision or research expertise. Several methods are used to convert dimension rankings into weights. The selection and ordering of dimensions differed between the two discussion groups, as did the resulting poverty measures. For instance, the poverty headcount using the dimensions and weights of the ‘lived experience’ group ranged from 20.61 to 26.96% as compared to a range of 18.62–33.19% using those of the ‘provider/researcher’ group. One of the main results of this study is that the Alkire Foster method is sensitive to the selection of dimensions and the methods used to derive rankings and weights. It points toward the limitation of relying exclusively on small scale qualitative methods for the selection and ranking of dimensions. In addition, the participatory framework used in this study was found to be essential in interpreting results, in particular with respect to the limitations of the data set in measuring relevant dimensions.