A CLASS OF LOGARITHMIC-CUM-EXPONENTIAL ESTIMATORS FOR POPULATION MEAN WITH RISK ANALYSIS USING DOUBLE SAMPLING.

In order to improve upon the efficiency of an estimate in double sampling for estimating population mean of character under study using an auxiliary variable, a part of survey resources are used to collect the information on auxiliary variable. Some authors have suggested exponential-type estimators and some others advocated for log-type estimators. But combination of such is required for specific situation. This paper presents a class of logarithmic-cum-exponential ratio estimators in double sampling setup. The expressions for the mean squared error and bias of the proposed class of estimators are derived for two different cases(sub-sample and independent sample). Sometimes the persons involved in the sample survey have to undergo for risk on life. For example, data collection in naxalites area, working in intense forest, interview during spread of epidemic or data collection in politically disturbed region. Such risk may affect the accuracy, efficiency of estimation. A linear Risk function is used for the proposed class of estimators. Two cases of double sampling are compared in terms of relative efficiency in view to risk aspect. It is found that the proposed class of estimators has a lower mean squared error than the simple mean estimator, usual ratio, usual exponential, usual log estimators in the double sampling setup. In addition, these theoretical results are supported by a numerical example. Risk function based simulated study is performed for the support of findings of the content. Optimal sample sizes under risk are derived and compared under two cases. [ABSTRACT FROM AUTHOR]