On weighted Renyi’s entropy for double-truncated distribution

In a recent paper, Nourbakhsh and Yari (2017 Nourbakhsh, M., and G. Yari. 2017. Weighted Renyi’s entropy for lifetime distributions. Communications in Statistics—Theory and Methods 46 (14):7085–98.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) introduce the weighted version of Renyi’s entropy for left/right truncated random variables and studied their properties in context of reliability analysis. In the present communication we extend the notion of weighted Renyi’s entropy for two-sided truncated random variable. In reliability theory and survival analysis, this measure may help to study the quantitative-qualitative information spectrum of a system/component when it fails between two time points. Various aspects of weighted Renyi’s interval entropy have been discussed and some mistakes in the preceding literature have also been corrected. These results generalize and enhance the related existing results that are developed based on weighted Renyi’s entropy for one-sided truncated random variable. Finally, a simulation study is added to provide the estimates of the proposed measure and to demonstrate the performance of the estimates.     

Estimation of population mean in successive sampling under super-population model in presence of random non response situations

The present work is an attempt to estimate the population mean on the current occasion in two-occasion successive (rotation) sampling in presence of random non response situations. The estimation strategy has been constructed under a super-population model design approach with the help of imputation technique. The estimators proposed on the current occasion cover the cases of occurrences random non responses on either of the occasions. Detail behaviors of the proposed class of estimators have been studied and its performance has been examined with the sample mean estimator. The results are demonstrated through empirical studies which establish the effectiveness of the proposed class of estimators. Suitable recommendations have been put forward to the survey statisticians for its practical application.     

Tracking multiple moving objects in images using Markov Chain Monte Carlo

A new Bayesian state and parameter learning algorithm for multiple target tracking models with image observations are proposed. Specifically, a Markov chain Monte Carlo algorithm is designed to sample from the posterior distribution of the unknown time-varying number of targets, their birth, death times and states as well as the model parameters, which constitutes the complete solution to the specific tracking problem we consider. The conventional approach is to pre-process the images to extract point observations and then perform tracking, i.e. infer the target trajectories. We model the image generation process directly to avoid any potential loss of information when extracting point observations using a pre-processing step that is decoupled from the inference algorithm. Numerical examples show that our algorithm has improved tracking performance over commonly used techniques, for both synthetic examples and real florescent microscopy data, especially in the case of dim targets with overlapping illuminated regions.     

JAMES-STEIN RULE ESTIMATORS IN LINEAR REGRESSION MODELS WITH MULTIVARIATE-t DISTRIBUTED ERROR

This paper considers estimation of β in the regression model y =Xβ+μ, where the error components in μ have the jointly multivariate Student-t distribution. A family of James-Stein type estimators (characterised by nonstochastic scalars) is presented. Sufficient conditions involving only X are given, under which these estimators are better (with respect to the risk under a general quadratic loss function) than the usual minimum variance unbiased estimator (MVUE) of β. Approximate expressions for the bias, the risk, the mean square error matrix and the variance-covariance matrix for the estimators in this family are obtained. A necessary and sufficient condition for the dominance of this family over MVUE is also given.     

Statistical analysis of intercropping data using a correlated error structure *

Intercropping is an important farming system, especially in tropical regions. A statistical model with competition coefficients and correlated error structure is suggested for the analysis of data from intercropping experiments involving two crop species. Data from an intercropping experiment with pearl millet and sorghum genotypes are used to illustrate the technique.     

An improved two stage randomized response strategy

Mangat and Singh (1990) have suggested a two stage randomized response technique to estimate the proportion of population possessing a sensitive attribute. The procedure was shown to be more efficient than the procedure due to Warner (1965). Recently, Tracy and Osahan (1993) have suggested a modification to the Mangat and Singh (1990) procedure which results in a more efficient strategy in practice. In this paper we propose a modification to the Tracy and Osahan (1993) procedure. The modified procedure is a generalization of Tracy and Osahan (1993) and is always more efficient than their strategy. An empirical study has also been undertaken to find the extent of relative efficiency.     

Contradictions in consciousness or variations in tradition: Hindu women in the South African diaspora

The introductory section of this paper reviews previous studies of the Indian diaspora to show their lack of attention to gender issues. While ideals of Hindu fundamentalism and social conditions imposed by caste are unlikely to be recreated in South Africa, it is proposed that Hindu women in South Africa are custodians of Hindu values. The paper goes on to present a brief history of middle and upper-class Hindu women in South Africa to place them within the context of the Indian diaspora. After describing the fieldwork and methodology (data were gathered from extensive interviews with 20 women representing the four major linguistic groups currently living in Durban), some of the distinctive characteristics of women's experiences and the problems these present because they are either contradictions or variations of conditions in India are discussed. The study then demonstrates that the individual choices made by the women are inconsistent with the apartheid notions of unambiguous social boundaries and also challenge the opposing Marxist perspective that ethnic consciousness is false. It is concluded that cultural adornments and self-imposed limitations on travel and socialization publicize status and ethnic identity and continuity with tradition. Hindu women in South Africa emphasize this continuity through personal beliefs or through the way they present themselves in public.     

Discrete optimization with polynomially detectable boundaries and restricted level sets

The paper describes an optimization procedure for a class of discrete optimization problems which is defined by certain properties of the boundary of the feasible region and level sets of the objective function. It is shown that these properties are possessed, for example, by various scheduling problems, including a number of well known NP-hard problems which play an important role in scheduling theory. For one of these problems the presented optimization procedure is compared with a version of the branch-and-bound algorithm by means of computational experiments.     

Book reviews

Abstract

Social Policy, Public Policy Meredith Edwards, Cosmo Howard, Robin Miller (2001), Allen & Unwin, Sydney ISBN 1 86448 9480 $35.00 RRP.

Spirituality in social work practice: Narratives for professional helping Sonia Abels (Ed) (2000), Love Publishing Company, Denver, Colorado 131 pp. $56.90 (paperback)

Family — centered policies and practices: International implications Katharine Briar-Lawson, Hal A. Lawson, Charles B. Hennon and Alan R. Jones, Columbia University Press, New York Chichester, West Sussex ISBN 0 231 12106 7 462 pp. (soft cover)

Lookin' after our own: Supporting Aboriginal families through the hospital experience Angela Clarke, Shawana Andrews and Neville Austin (2000), A report sponsored by the Victorian Health Promotion Foundation

Making stepfamilies work A course for couples Irene Gerrard & Margaret Howden (1998), Stepfamily Association of Victoria Inc. ISBN 0 646 3622 4 (spiral bound)

The empowerment approach to social work practice: Building the beloved community Judith AS Lee (2001), Columbia University Press, New York, ISBN 0 231 11548 2 517 pp. (hardback)