Tests of normality based on EDF statistics using partially rank ordered set sampling designs

Year 2021, Volume: 13 Issue: 2, 52 - 73, 01.07.2021

Yusuf Can Sevil Tuğba Yıldız

Abstract

In this study, we considered five goodness-of-fit (GOF) tests based on empirical distribution function (EDF) which are Kolmogorov-Smirnov (D), Kuiper (V ), Cram´er-von Mises (W2), Watson (U2), Anderson-Darling (A2) tests to assess normality. Thus, we first suggested the EDFs based partially rank ordered set (PROS) sampling designs which are known as PROS Level-0, Level-1 and Level-2 sampling designs. Then, we discussed the relative efficiencies of the suggested EDFs w.r.t their counterparts of simple random sampling (SRS) and ranked set sampling (RSS). The main idea of this study is to compare the performances of the five different GOF tests based on PROS sampling designs with the GOF tests based on SRS and RSS. For this purpose, we investigated the power of the suggested GOF tests based on PROS sampling designs by performing simulations. In addition to the simulations, a real data set is considered to illustrate the GOF tests based on PROS sampling designs. According to the results, it can be seen that the EDFs based on PROS sampling designs are more efficient than the EDFs based on SRS and RSS. Also, it is clearly appeared that the GOF tests, Kolmogorov-Smirnov (D), Cram´er-von Mises (W2) and Anderson- Darling (A2), based on PROS sampling designs has the best power performance.

Keywords

Ranked set sampling, Partially rank ordered set, Sampling designs, Empirical distribution function, Type I error;, Goodness-of-fit tests, Power of test

Project Number

2018.KB.FEN.003

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