Estimating of the distribution function under ranked set sampling with unequal probabilities


Sevil Y. C., Yıldız T.

12th International Statistics Days Congress (ISDC2022), İzmir, Turkey, 13 - 16 October 2022

  • Publication Type: Conference Paper / Unpublished
  • City: İzmir
  • Country: Turkey
  • Dokuz Eylül University Affiliated: Yes

Abstract

Ranked set sampling (RSS), suggested by McIntyre (1952), is a popular sampling strategy when the measurements of the sample units are relatively difficult (expensive and/or time-consuming). The estimation of distribution function has received considerable attention in the literature of RSS. Because many practical problems involve estimation of distribution function from experimental data. Many authors have proposed empirical distribution functions (EDFs) based on RSS and its modifications (see, for example, Stokes and Sager, 1988; Samawi and Al-Sagher, 2001, Nazari et al., 2016 and Zamanzade, 2019). For finite population setting, there are a few studies on estimation of distribution function (see, for example, Sevil and Yildiz, 2017, 2020; Yildiz and Sevil, 2019). In this study, design-based estimators for distribution function have been developed using RSS designs (level-0, level-1 and level-2). Some of their asymptotic properties have been investigated. Theoretical and numerical results show that the level-2 sampling design provides a more efficient EDF estimator than its counterparts of level-0, leve-1 and simple random sampling.