Effective Estimation Methods Through Ranked Set Sampling for Mixture Model: Industrial and Survival Applications

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DOI: https://doi.org/10.28924/2291-8639-23-2025-286
Published: Nov 13, 2025
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Amal S. Hassan, Doaa M. H. Ahmed, Ehab M. Almetwally, Mohammed Elgarhy, Ahmed M. Gemeay, Effective Estimation Methods Through Ranked Set Sampling for Mixture Model: Industrial and Survival Applications, Int. J. Anal. Appl., 23 (2025), 286.

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Amal S. Hassan, Doaa M. H. Ahmed, Ehab M. Almetwally, Mohammed Elgarhy, Ahmed M. Gemeay

Abstract

The sampling strategy has a considerable impact on the representativeness of the sampled data and can lead to incorrect estimates if not carefully chosen. An improved method over more conventional simple random sampling (SRS) is ranked set sampling (RSS). The RSS is more efficient, reducing the number of measurements needed for a desired level of precision, especially in challenging data collection scenarios. The Monsef distribution is a recent mixture lifetime model that has demonstrated effectiveness in modeling various real-world datasets. Several mathematical aspects of the Monsef distribution include quantiles, upper incomplete moments, lower incomplete moments, stochastic ordering, and extropy measures. This work investigates the use of RSS in conjunction with several traditional estimation techniques to estimate the parameters of the Monsef distribution. Fifteen different estimation procedures are investigated, including maximum product spacing, some minimum spacing distance methods, the Kolmogorov method, ordinary least squares, maximum likelihood, and weighted least squares. To assess the performance of the estimation techniques for a range of sample sizes under perfect ranking conditions and both sampling techniques, a simulation scenario is conducted. The partial and total ranks of numerous estimates are displayed to determine the best estimation approach. According to simulation results, the maximum likelihood and maximum product spacing approaches consistently outperform other methods in evaluating the estimated quality for both RSS and SRS. To demonstrate the feasibility of the different methods, three authentic datasets from various fields are examined.

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References

  1. K. Pearson, III. Contributions to the Mathematical Theory of Evolution, Philos. Trans. R. Soc. Lond. 185 (1894), 71–110. https://doi.org/10.1098/rsta.1894.0003.
  2. D.V. Lindley, Fiducial Distributions and Bayes' Theorem, J. R. Stat. Soc. Ser. B: Stat. Methodol. 20 (1958), 102–107. https://doi.org/10.1111/j.2517-6161.1958.tb00278.x.
  3. S. Sen, S.S. Maiti, N. Chandra, The Xgamma Distribution: Statistical Properties and Application, J. Mod. Appl. Stat. Methods 15 (2016), 774–788. https://doi.org/10.22237/jmasm/1462077420.
  4. P. Jordanova, J. Dušek, M. Stehlík, Microergodicity Effects on Ebullition of Methane Modelled by Mixed Poisson Process with Pareto Mixing Variable, Chemom. Intell. Lab. Syst. 128 (2013), 124–134. https://doi.org/10.1016/j.chemolab.2013.08.006.
  5. R. Shanker, Shanker Distribution and Its Applications, Int. J. Stat. Appl. 5(2015), 338–348.
  6. M.M.E. Abd El-Monsef, M.M. Abd El-Raouf, Rayleigh-Half Normal Distribution for Modeling Tooth Movement Data, J. Biopharm. Stat. 30 (2019), 481–494. https://doi.org/10.1080/10543406.2019.1684312.
  7. R. Shanker, Rama Distribution and Its Application, Int. J. Stat. Appl. 7 (2017), 26–35.
  8. A.S. Hassan, A.M. Abd-Elfattah, M.M. Hassan, Bayesian Analysis for Mixture of Burr XII and Burr X Distributions, Far East J. Math. Sci. 103 (2018), 1031–1041. https://doi.org/10.17654/ms103061031.
  9. C.K. Onyekwere, O.J. Obulezi, Chris-Jerry Distribution and Its Applications, Asian J. Probab. Stat. 20 (2022), 16–30. https://doi.org/10.9734/ajpas/2022/v20i130480.
  10. M.M.E. Abd El-Monsef, Erlang Mixture Distribution with Application on COVID-19 Cases in Egypt, Int. J. Biomath. 14 (2021), 2150015. https://doi.org/10.1142/s1793524521500157.
  11. A. Mustafa, M.M.E. Abd El-Monsef, The Weighted Monsef Distribution, Afr. J. Math. Comput. Sci. Res. 13 (2020), 74–84.
  12. M.M.E. Abd El-Monsef, N.M. Sohsah, W.A. Hassanein, Unit Monsef Distribution with Regression Model, Asian J. Probab. Stat. 15 (2021), 330–340. https://doi.org/10.9734/ajpas/2021/v15i430384.
  13. M.M.E. Abd El-Monsef, E.I. Soliman, M.A. El-Qurashi, Stress-Strength Reliability for Monsef Distribution, J. Stat. Appl. Probab. 13 (2024), 1107–1126. https://doi.org/10.18576/jsap/130320.
  14. G. McIntyre, A Method for Unbiased Selective Sampling, Using Ranked Sets, Aust. J. Agric. Res. 3 (1952), 385–390. https://doi.org/10.1071/ar9520385.
  15. K. Takahasi, K. Wakimoto, On Unbiased Estimates of the Population Mean Based on the Sample Stratified by Means of Ordering, Ann. Inst. Stat. Math. 20 (1968), 1–31. https://doi.org/10.1007/bf02911622.
  16. G.P. Patil, A.K. Sinha, C. Taille, Relative Precision of Ranked Set Sampling: A Comparison with the Regression Estimator, Environmetrics 4 (1993), 399–412. https://doi.org/10.1002/env.3170040404.
  17. M. Mahdizadeh, E. Zamanzade, Efficient Body Fat Estimation Using Multistage Pair Ranked Set Sampling, Stat. Methods Med. Res. 28 (2017), 223–234. https://doi.org/10.1177/0962280217720473.
  18. E.G. Koçyiğit, C. Kadilar, Information Theory Approach to Ranked Set Sampling and New Sub-Ratio Estimators, Commun. Stat. - Theory Methods 53 (2022), 1331–1353. https://doi.org/10.1080/03610926.2022.2100910.
  19. A.S. Hassan, N. Alsadat, M. Elgarhy, H. Ahmad, H.F. Nagy, On Estimating Multi- Stress Strength Reliability for Inverted Kumaraswamy Under Ranked Set Sampling with Application in Engineering, J. Nonlinear Math. Phys. 31 (2024), 30. https://doi.org/10.1007/s44198-024-00196-y.
  20. H. Muttlak, W. Al-Sabah, Statistical Quality Control Based on Ranked Set Sampling, J. Appl. Stat. 30 (2003), 1055–1078. https://doi.org/10.1080/0266476032000076173.
  21. H. NAGY, A. HASSAN, Reliability Estimation in Multicomponent Stress-Strength for Generalized Inverted Exponential Distribution Based on Ranked Set Sampling, Gazi Univ. J. Sci. 35 (2022), 314–331. https://doi.org/10.35378/gujs.760469.
  22. X. He, W. Chen, W. Qian, Maximum Likelihood Estimators of the Parameters of the Log-Logistic Distribution, Stat. Pap. 61 (2018), 1875–1892. https://doi.org/10.1007/s00362-018-1011-3.
  23. A. Adatia, Estimation of Parameters of the Half-Logistic Distribution Using Generalized Ranked Set Sampling, Comput. Stat. Data Anal. 33 (2000), 1–13. https://doi.org/10.1016/s0167-9473(99)00035-3.
  24. H.J. Khamnei, S. Abusaleh, Estimation of Parameters in the Generalized Logistic Distribution Based on Ranked Set Sampling, Int. J. Nonlinear Sci. 24 (2017), 154–160.
  25. H. Fei, B.K. Sinha, Z. Wu, EStimation of Parameters in Two-Parameter Weibull and Extreme-Value Distributions Using a Ranked Set Sample, J. Stat. Res. 28 (1994), 149–161.
  26. M. Esemen, S. Gürler, Parameter Estimation of Generalized Rayleigh Distribution Based on Ranked Set Sample, J. Stat. Comput. Simul. 88 (2017), 615–628. https://doi.org/10.1080/00949655.2017.1398256.
  27. F.G. Akgül, Ş. Acıtaş, B. Şenoğlu, Inferences on Stress–Strength Reliability Based on Ranked Set Sampling Data in Case of Lindley Distribution, J. Stat. Comput. Simul. 88 (2018), 3018–3032. https://doi.org/10.1080/00949655.2018.1498095.
  28. R. Bantan, A.S. Hassan, M. Elsehetry, B.M.G. Kibria, Half-Logistic Xgamma Distribution: Properties and Estimation Under Censored Samples, Discret. Dyn. Nat. Soc. 2020 (2020), 9136513. https://doi.org/10.1155/2020/9136513.
  29. V.C. Pedroso, C.A. Taconeli, S.R. Giolo, Estimation Based on Ranked Set Sampling for the Two-Parameter Birnbaum–Saunders Distribution, J. Stat. Comput. Simul. 91 (2020), 316–333. https://doi.org/10.1080/00949655.2020.1814287.
  30. M.M. Yousef, A.S. Hassan, A.H. Al-Nefaie, E.M. Almetwally, H.M. Almongy, Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling, Mathematics 10 (2022), 3122. https://doi.org/10.3390/math10173122.
  31. A.S. Hassan, R.S. Elshaarawy, H.F. Nagy, Parameter Estimation of Exponentiated Exponential Distribution Under Selective Ranked Set Sampling, Stat. Transit. New Ser. 23 (2022), 37–58. https://doi.org/10.2478/stattrans-2022-0041.
  32. H.F. Nagy, A.I. Al-Omari, A.S. Hassan, G.A. Alomani, Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data, Mathematics 10 (2022), 4102. https://doi.org/10.3390/math10214102.
  33. N. Alsadat, A.S. Hassan, A.M. Gemeay, C. Chesneau, M. Elgarhy, Different Estimation Methods for the Generalized Unit Half-Logistic Geometric Distribution: Using Ranked Set Sampling, AIP Adv. 13 (2023), 085230. https://doi.org/10.1063/5.0169140.
  34. A. Hassan, R. Elshaarawy, H. Nagy, Estimation Study of Multicomponent Stress-Strength Reliability Using Advanced Sampling Approach, Gazi Univ. J. Sci. 37 (2024), 465–481. https://doi.org/10.35378/gujs.1132770.
  35. A.S. Hassan, N. Alsadat, M. Elgarhy, C. Chesneau, R. Elmorsy Mohamed, Different Classical Estimation Methods Using Ranked Set Sampling and Data Analysis for the Inverse Power Cauchy Distribution, J. Radiat. Res. Appl. Sci. 16 (2023), 100685. https://doi.org/10.1016/j.jrras.2023.100685.
  36. N. Alsadat, A.S. Hassan, A.M. Gemeay, C. Chesneau, M. Elgarhy, Different Estimation Methods for the Generalized Unit Half-Logistic Geometric Distribution: Using Ranked Set Sampling, AIP Adv. 13 (2023), 085230. https://doi.org/10.1063/5.0169140.
  37. S.A. Alyami, A.S. Hassan, I. Elbatal, N. Alotaibi, A.M. Gemeay, et al., Estimation Methods Based on Ranked Set Sampling for the Arctan Uniform Distribution with Application, AIMS Math. 9 (2024), 10304–10332. https://doi.org/10.3934/math.2024504.
  38. N. Alsadat, A.S. Hassan, M. Elgarhy, A. Johannssen, A.M. Gemeay, Estimation Methods Based on Ranked Set Sampling for the Power Logarithmic Distribution, Sci. Rep. 14 (2024), 17652. https://doi.org/10.1038/s41598-024-67693-4.
  39. M. Shaked, J.G. Shanthikumar, Stochastic Orders, Springer, 2007.
  40. F. Lad, G. Sanfilippo, G. Agrò, Extropy: Complementary Dual of Entropy, Stat. Sci. 30 (2015), 40–58. https://doi.org/10.1214/14-sts430.
  41. N. Balakrishnan, F. Buono, M. Longobardi, On Weighted Extropies, Commun. Stat. - Theory Methods 51 (2020), 6250–6267. https://doi.org/10.1080/03610926.2020.1860222.
  42. D.A. Wolfe, Ranked Set Sampling: Its Relevance and Impact on Statistical Inference, ISRN Probab. Stat. 2012 (2012), 568385. https://doi.org/10.5402/2012/568385.
  43. B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A First Course in Order Statistics, SIAM, (1992).
  44. Cheng, R.C.H.; Amin, N.A.K. Maximum Product-of-Spacings Estimation With Applications to the Log-Normal Distribution, Technical Report, Department of Mathematics, University of Wales, 1979.
  45. A.M. Nigm, E.K. Al-Hussaini, Z.F. Jaheen, Bayesian One-Sample Prediction of Future Observations Under Pareto Distribution, Statistics 37 (2003), 527–536. https://doi.org/10.1080/02331880310001598837.
  46. E.A. Ahmed, Z. Ali Alhussain, M.M. Salah, H. Haj Ahmed, M.S. Eliwa, Inference of Progressively Type-Ii Censored Competing Risks Data from Chen Distribution with an Application, J. Appl. Stat. 47 (2020), 2492–2524. https://doi.org/10.1080/02664763.2020.1815670.
  47. B. Saraçoğlu, I. Kinaci, D. Kundu, On Estimation of $R= P (Y< X)$ for Exponential Distribution Under Progressive Type-II Censoring, J. Stat. Comput. Simul. 82 (2012), 729–744. https://doi.org/10.1080/00949655.2010.551772.