A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information |
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Authors: | Housila P Singh Sarjinder Singh Marcin Kozak |
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Institution: | (1) School of Studies in Statistics, Vikram University, Ujjain, 456010, MP, India;(2) Department of Mathematics, University of Texas at Brownsville and Texas Southmost College, Brownsville, TX 78520, USA;(3) Department of Experimental Design and Bioinformatics, Faculty of Agriculture and Biology, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776 Warsaw, Poland |
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Abstract: | This paper considers the problem of estimating the finite-population distribution function and quantiles with the use of auxiliary
information at the estimation stage of a survey. We propose the families of estimators of the distribution function of the
study variate y using the knowledge of the distribution function of the auxiliary variate x. In addition to ratio, product and difference type estimators, many other estimators are identified as members of the proposed
families. For these families the approximate variances are derived, and in addition, the optimum estimator is identified along
with its approximate variance. Estimators based on the estimated optimum values of the unknown parameters used to minimize
the variance are also given with their properties. Further, the family of estimators of a finite-population distribution function
using two-phase sampling is given, and its properties are investigated.
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Keywords: | Auxiliary variate Distribution function Finite population Study variate Two-phase sampling |
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