On length and area-biased Maxwell distributions

This article addresses the various properties and different methods of estimation of the unknown parameter of length and area-biased Maxwell distributions. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of length and area-biased Maxwell distributions (such as moments, moment-generating function (mgf), hazard rate function, mean residual lifetime function, residual lifetime function, reversed residual life function, conditional moments and conditional mgf, stochastic ordering, and measures of uncertainty) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimator, moments estimator, least-square and weighted least-square estimators, maximum product of spacings estimator and compare them using extensive numerical simulations. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using inverted gamma prior for the scale parameter. Furthermore, Bayes estimators and their respective posterior risks are computed and compared using Markov chain Monte Carlo (MCMC) algorithm. Also, bootstrap confidence intervals using frequentist approaches are provided to compare with Bayes credible intervals. Finally, a real dataset has been analyzed for illustrative purposes.     

On Using Negative Binomial Distribution as a Randomization Device in Sensitive Surveys

In this article, an interesting improvement of some recent randomized response techniques has been proposed. The proposed randomized response technique applies Negative Binomial distribution to obtain data from respondents. An unbiased estimator of proportion of a sensitive attribute has been suggested and it is shown, numerically, that the new estimator performs better than the recent estimators while doing a sensitive survey. It is also established that the proposed estimator is unconditionally better than that of the estimator based on using the geometric distribution.     

Risk analysis of fast spreading species in a Kashmir Himalayan National Park (Dachigam) for better monitoring and management

Huge economic costs and ecological impacts of invasive alien species (IAS) in the protected areas (PAs) worldwide make their timely prediction and potential risk assessment of central importance for effective management. While the preborder weed risk assessment framework has been extensively evaluated and implemented, the postborder species risk assessment framework has not been subjected to the same degree of scrutiny. Here we used a rather more realistic modified version of the Australian Weed Risk framework (AWRM) for Dachigam National Park (DNP) in Kashmir Himalaya against 84 plant species, including 55 alien species and 29 fast spreading native species, for risk analysis. We found two very high-risk species, three high-risk species, 10 medium-risk species, 29 low-risk species, and 40 negligible-risk species in the DNP. The containment scores accordingly ranged from 14.4 to 293.5 comprising of 27 species that can be contained with very high feasibility, 23 species with high feasibility, 14 species with medium feasibility, and 12 species which cannot be contained easily thereby having low feasibility of containment (FOC) score. However, eight species which have a negligible FOC score are difficult to contain within their infestation sites. Our results demonstrate the merit of the AWRM with a caution that the necessary region-specific modifications may help in its better implementation. Overall, these results provide quite a promising tool in the hands of protected area managers to timely and effectively deal with the problem of plant invasions.     

A new estimator of finite population mean based on the dual use of the auxiliary information

When a sufficient correlation between the study variable and the auxiliary variable exists, the ranks of the auxiliary variable are also correlated with the study variable, and thus, these ranks can be used as an effective tool in increasing the precision of an estimator. In this paper, we propose a new improved estimator of the finite population mean that incorporates the supplementary information in forms of: (i) the auxiliary variable and (ii) ranks of the auxiliary variable. Mathematical expressions for the bias and the mean-squared error of the proposed estimator are derived under the first order of approximation. The theoretical and empirical studies reveal that the proposed estimator always performs better than the usual mean, ratio, product, exponential-ratio and -product, classical regression estimators, and Rao (1991 Rao, T.J. (1991). On certail methods of improving ration and regression estimators. Commun. Stat. Theory Methods 20(10):3325–3340.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Singh et al. (2009 Singh, R., Chauhan, P., Sawan, N., Smarandache, F. (2009). Improvement in estimating the population mean using exponential estimator in simple random sampling. Int. J. Stat. Econ. 3(A09):13–18. [Google Scholar]), Shabbir and Gupta (2010 Shabbir, J., Gupta, S. (2010). On estimating finite population mean in simple and stratified random sampling. Commun. Stat. Theory Methods 40(2):199–212.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), Grover and Kaur (2011 Grover, L.K., Kaur, P. (2011). An improved estimator of the finite population mean in simple random sampling. Model Assisted Stat. Appl. 6(1):47–55. [Google Scholar], 2014) estimators.     

Social determinants of under-five mortality in urban Bangladesh

Journal of Population Research - Rapid urbanization and persistent health inequity are two significant phenomena in contemporary developing world. Urban population, albeit with more modern...     

Generalized geometric distribution of order k: A flexible choice to randomize the response

This article focuses on the improvement of a well-celebrated randomized response technique of Kuk. A generalized randomized response technique is suggested. In particular, the generalized geometric distribution of order k is introduced as a randomization device for estimating the population proportion of a rare sensitive attribute. The proposed randomized response technique includes Singh and Grewal and Hussain et al. techniques as its special cases. Through numerical illustrations, it is established that the suggested technique is superior to the Kuk, Singh and Grewal, and Hussain et al. techniques. Flexibility of the proposed technique is also discussed.     

The inverted Nadarajah–Haghighi distribution: estimation methods and applications

The inverted (or inverse) distributions are sometimes very useful to explore additional properties of the phenomenons which non-inverted distributions cannot. We introduce a new inverted model called the inverted Nadarajah–Haghighi distribution which exhibits decreasing and unimodal (right-skewed) density while the hazard rate shapes are decreasing and upside-down bathtub. Our main focus is the estimation (from both frequentist and Bayesian points of view) of the unknown parameters along with some mathematical properties of the new model. The Bayes estimators and the associated credible intervals are obtained using Markov Chain Monte Carlo techniques under squared error loss function. The gamma priors are adopted for both scale and shape parameters. The potentiality of the distribution is analysed by means of two real data sets. In fact, it is found to be superior in its ability to sufficiently model the data as compared to the inverted Weibull, inverted Rayleigh, inverted exponential, inverted gamma, inverted Lindley and inverted power Lindley models.     

A personal reflection of risking and protecting lives during the third wave of the coronavirus pandemic

In this paper, I engage with my personal experiences and reflections regarding my fear of exposure to coronavirus in a collective and physically demonstrative society. I reflect on my ongoing struggle of coping with social and cultural pressures, for example, the avoidance of ‘touch’ that demonstrates care and affection irrespective of whether someone is ill with the virus. Developed during the third wave of the pandemic, this paper reveals the ambivalence and the emotional challenges involved therein as I tried to (re)negotiate social interactions. It reflects the resistance and denial of the people that coronavirus even exists as they tried to justify their illness by linking it with other known diseases. Hence, the majority disapproved of social distancing to avoid stigmatization and being distanced from others. I believe that expressions of ‘care’ and ‘affection’ requires reconsideration in such circumstances as an act of care itself to protect lives.