Estimation of rare and clustered population variance in adaptive cluster sampling

Abstract

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.     

A double acceptance sampling plan for generalized log-logistic distributions with known shape parameters

A double acceptance sampling plan for the truncated life test is developed assuming that the lifetime of a product follows a generalized log-logistic distribution with known shape parameters. The zero and one failure scheme is mainly considered, where the lot is accepted if no failures are observed from the first sample and it is rejected if two or more failures occur. When there is one failure from the first sample, the second sample is drawn and tested for the same duration as the first sample. The minimum sample sizes of the first and second samples are determined to ensure that the true median life is longer than the given life at the specified consumer’s confidence level. The operating characteristics are analyzed according to various ratios of the true median life to the specified life. The minimum such ratios are also obtained so as to lower the producer’s risk at the specified level. The results are explained with examples.     

Understanding the pattern of support for the elderly: a comparison between Israel and Sweden

Cross-cultural comparison can offer critical input to analyses of the interplay between formal and informal services for the elderly. Israel and Sweden have very different population structures and represent different points on the spectrum of welfare state development: Sweden has a much higher percentage of elderly, a less traditional family structure, and a much more developed system of public support. In addition, there are thought to be different attitudes toward family ties, with a less family-oriented value structure in Sweden. The natural question is to what extent these differences translate into differences in the extent and nature of family support for the elderly. In this article, family structure, living arrangements, disability rates, and formal and informal sources of help in Sweden and Israel are compared at various points in time. While there is a greater rate of formal service provision in Sweden and some substitution for family support seems to have occurred, informal care has nevertheless remained important. In both countries, residential patterns are critical: it is when the elderly live alone that the formal system has tended to replace the family. The rate of institutionalization is particularly important in determining the rate of disabled elderly requiring care, both formal and informal, in the community.     

Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

Most of the research work in the theory of survey sampling only deals with the sampling errors under the assumptions: (i) there is a complete response and (ii) recorded information from individuals is correct but in practice it is not always true. Non-sampling errors like non-response and measurement errors (MEs) mostly creep into the survey and become more influential for estimators than sampling errors. Considering this practical situation of non-response and MEs jointly, we proposed an optimum class of estimators for population mean under simple random sampling using conventional and non-conventional measures. Bias and mean square error of the proposed estimators are derived up to first degree of approximation. Moreover, a simulation study is conducted to assess the performance of new estimators which proves that proposed estimators are more efficient than the traditional Hansen and Hurwitz estimator and other competing estimators.     

Bayesian inference for the randomly censored Burr-type XII distribution

The article presents the Bayesian inference for the parameters of randomly censored Burr-type XII distribution with proportional hazards. The joint conjugate prior of the proposed model parameters does not exist; we consider two different systems of priors for Bayesian estimation. The explicit forms of the Bayes estimators are not possible; we use Lindley's method to obtain the Bayes estimates. However, it is not possible to obtain the Bayesian credible intervals with Lindley's method; we suggest the Gibbs sampling procedure for this purpose. Numerical experiments are performed to check the properties of the different estimators. The proposed methodology is applied to a real-life data for illustrative purposes. The Bayes estimators are compared with the Maximum likelihood estimators via numerical experiments and real data analysis. The model is validated using posterior predictive simulation in order to ascertain its appropriateness.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.     

Progressive Variance Control Charts for Monitoring Process Dispersion

In a process, the deviation from location or scale parameters affects the quality of the process and waste resources. So it is essential to monitor such processes for possible changes due to any assignable causes. Control charts are the most famous tool used to meet this intention. It is useless to monitor process location until the assurance that process dispersion is in-control. This study proposes some new two-sided memory control charts named as progressive variance (PV) control charts which are based on sample variance to monitor changes in process dispersion assuming normality of quality characteristic to be monitored. Simulation studies are made, and an example is discussed to evaluate the performance of the proposed charts. The comparison of the proposed chart is made with exponentially weighted moving average- and cumulative sum-type charts for process dispersion. The study shows that performance of the proposed charts are uniformly better than its competitors for detecting positive shifts while for detecting negative shift in the variance their performance is better for small shifts and reasonably good for moderated shifts.     

On the estimation of parameters,survival functions,and hazard rates based on fuzzy life time data

Life time data analysis is regarded as one of the significant out-shoots of statistics. Classical statistical techniques reckon life time observations as precise numbers and solely cover variation among the observations. In fact, there are two types of uncertainty in data: variation among the observations and the fuzziness. To this effect, the analysis techniques, which do not consider fuzziness and are only based on precise life time observations, use incomplete information; hence lead to pseudo results. This study aimed at generalizing parameters estimation, survival functions, and hazard rates for fuzzy life time data.     

An Explicit Distribution to Model the Proportion of Heating Degree Day and Cooling Degree Day

With a view to estimating the energy consumption, we derive the explicit distribution of the proportion X/(X + Y) when X and Y follow the new Bivariate Affine-Linear Exponential distribution. An application of this distribution to model the proportion of heating using the heating degree day and the cooling degree day data in the State of Alabama for Appalachian Mountain is provided. Using intensive computations based on R-program, tabulation of some quantiles associated with this particular distribution of proportion is also provided, which is quite useful in estimating the proportion of energy required to heat a building.     

Locally D-Optimal Design for a Logit Model in Discrete Choice Experiment

Conjoint analysis is concerned with understanding how people make choice between products or services (alternatives) or a combination of product and service (choice set), so that businesses can design new products or services that better meet customers needs. In this situation, logit model (Multinomial Logit Model) has been used to calculate the probability related to choosing an alternative in a choice set with the highest utility. Then I considered several choice sets instead of one. In this article, I have used the locally D-optimal design for the combination of the level of attributes (two attributes each with two levels) to create alternatives. The optimal combination of alternatives in choice sets which help us to have a suitable choice.