A class of ratio cum product-type estimator is proposed in case of double sampling in the present paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight 'a' and 8 good range of a-values. it is found that the proposed estimator is more efficient than the set of estimator viz., simple mean estimator, usual ratio and product eetimators, ~BIVASTAVA'S estimator (1967), CHAKARBARTY'~ estimator and product-type estimator, which am in fact the particular cues of it. The proposed estimator is 8s efficient u linear regression estimator in double sampling a t optimum value of a. K e y words: Double sampling, cost-function, preliminary sample.
The problem of estimating the population mean using an auxiliary informetion has been dealt with in literature quite extensively. Ratio, product, linear regremion and ratio-type eetimators are well known. A o l w of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight 'a' and good range of a-valuea, i t is found that the proposed eetimator is superior than a set of estimators (i.e.. sample mean, usual ratio and product estimators, SBIVASTAVA'S (1967) estimator, CH~KSABARTY'S (1979) estimator and a product-type estimator) which are, in feet, the particular cases of it. A t optimum value of a, the proposed estimator is as efficient as linear regreasion estimator.
There are two caees in double sampling; ceee(i) when the eecond sample is a sub-aample from preliminary large sample. and ccree(ii) when the eeoond sample is not a nub-sample from the preliminary large sample. Remntly SIsODIA and DWIWDI (1981) propoeed a ratio cum product-type estimator in double sampling in whioh they have studied the properties of thiu estimator under case (i). In thie paper, we have made an attempt to study the properties of the same estimator under ~8 8 8(ii). It ie found that the estimator is superior than double sampling linear regreesion eatimator. umal ratio sethator, product estimator and among others. The estimator ie 81x1 compared with simple mean per unit for a given coet of the survey.
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