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A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

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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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Authors and Affiliations

  1. School of Studies in Statistics, Vikram University, Ujjain, 456010, MP, India

    Housila P. Singh

  2. Department of Mathematics, University of Texas at Brownsville and Texas Southmost College, Brownsville, TX, 78520, USA

    Sarjinder Singh

  3. Department of Experimental Design and Bioinformatics, Faculty of Agriculture and Biology, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776, Warsaw, Poland

    Marcin Kozak

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  1. Housila P. Singh
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  2. Sarjinder Singh
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  3. Marcin Kozak
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Correspondence to Marcin Kozak.

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Singh, H.P., Singh, S. & Kozak, M. A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information. Acta Appl Math 104, 115–130 (2008). https://doi.org/10.1007/s10440-008-9243-1

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