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Journals / Türkiye İstatistik Derneği İstatistik Dergisi / 2021 / Cilt: 13 - Sayı: 2

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

Yusuf Can SEVİL
Tuğba YILDIZ
Pages
52–73
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

SEVİL, Y. C., YILDIZ, T. (2021). Tests of normality based on EDF statistics using partially rank ordered set sampling designs. Türkiye İstatistik Derneği İstatistik Dergisi, Cilt: 13 - Sayı: 2, 52–73. https://ajindex.com/articles/812550

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References (15)

  1. McIntyre, G.A. (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3(4), 385-390.
  2. Takahasi, K. and Wakimoto, K. (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 20(1), 1-31.
  3. Dell, T. and Clutter, J. (1972). Ranked set sampling theory with order statistics background. Biometrics, 545-555.
  4. Kaur, A., Patil, G., Sinha, A. and Taillie, C. (1995). Ranked set sampling: an annotated bibliography. Environmental and Ecological Statistics, 2(1), 25-54.
  5. Chen, Z., Bai, Z. and Sinha, B. (2003). Ranked set sampling: theory and applications. Springer Science & Business Media. Al-Omari, A. I. and Bouza, C. N. (2014). Review of ranked set sampling: modifications and applications. Revista Investigaci´on Operacional, 3, 215-240.
  6. Deshpande, J. V. and Frey, J. and Ozturk, O. (2006). Nonparametric ranked-set sampling confidence intervals for quantiles of a finite population. Environmental and Ecological Statistics, 13(1), 25-40.
  7. Al-Saleh, M. F. and Samawi, H. M. (2007). A note on inclusion probability in ranked set sampling and some of its variations. Test, 16(1), 198-209.
  8. Ozdemir, Y. A. and Gokpinar, F. (2007). A generalized formula for inclusion probabilities in ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 36(1), 89-99.
  9. Ozdemir, Y. A. and Gokpinar, F. (2008). A new formula for inclusion probabilities in median ranked set sampling. Communication in Statistics- Theory and Methods, 37(13), 2022-2033.
  10. Gokpinar, F, Ozdemir, Y. A. (2010). Generalization of inclusion probabilities in ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 39(1), 89-95.
  11. Frey, J. (2011). Recursive computation of inclusion probabilities in ranked set sampling. Journal of Statistical Planning and Inference, 141(11), 3632-3639.
  12. Jafari Jozani, M., Johnson, B. C. (2011). Design based estimation for ranked set sampling in finite population. Environmental and Ecological Statistics, 18(4), 663-685.
  13. Jafari Jozani, M., Johnson, B. C. (2011). Randomized nomination sampling in finite populations. Journal of Statistical Planning and inference, 142(7), 2103-2115.
  14. Stokes, S L. and Sager, T. W. (1988). Characterization of a ranked-set sample with application to estimating distribution functions. Journal of the American Statistical Association, 83(402), 374-381.
  15. Frey, J. andWang, L. (2014). EDF-based goodness-of-