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Journals / Istatistik Journal of The Turkish Statistical Association / 2026 / Volume: 13 Issue: 2

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

Yusuf Can Sevil(DOKUZ EYLÜL ÜNİVERSİTESİ)
Tuğba Yıldız(DOKUZ EYLÜL ÜNİVERSİTESİ)
Pages
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Publication Date
2021-07-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ranked set sampling · Partially rank ordered set · Sampling designs

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.

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Cite This Article

Sevil, Y. C., Yıldız, T. (2021). Tests of normality based on EDF statistics using partially rank ordered set sampling designs. Istatistik Journal of The Turkish Statistical Association, Volume: 13 Issue: 2. https://ajindex.com/articles/1636466

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