Bayesian inference for the inverse Weibull distribution based on symmetric and asymmetric balanced loss functions with application

Hasaballah, Mustafa M.; Tashkandy, Yusra A.; Balogun, Oluwafemi Samsin; Bakr, M. E.

doi:10.17531/ein/187158

Artykuł - szczegóły

Tytuł artykułu

Bayesian inference for the inverse Weibull distribution based on symmetric and asymmetric balanced loss functions with application

Autorzy

Hasaballah Mustafa M. , Tashkandy Yusra A. , Balogun Oluwafemi Samsin , Bakr M. E.

Treść / Zawartość

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DOI

10.17531/ein/187158

Warianty tytułu

Języki publikacji

Abstrakty

In this study, the unified hybrid censored approach is employed to estimate the parameters of the inverse Weibull distribution, as well as the survival and hazard rate functions. Parameter estimates are obtained using both Bayesian and maximum likelihood approaches, with Bayesian estimates acquired through Lindley’s approximation method using three distinct balanced loss functions. These encompass both symmetric and asymmetric balanced loss functions, specifically the balanced squared error (BSE) loss function, the balanced linear exponential (BLINEX) loss function, and the balanced general entropy (BGE) loss function. We conduct a simulation study to compare the effectiveness of various estimators, and a real-world data analysis is presented to illustrate practical implementation. Ultimately, our findings indicate that Bayesian parameter estimates consistently outperform their maximum likelihood counterparts across all methods.

Słowa kluczowe

bayesian estimation Lindley's approximation inverse Weibull distribution maximum likelihood estimation unified hybrid censoring schemes symmetric balanced loss functions asymmetric balanced loss functions

Wydawca

Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne

Czasopismo

Eksploatacja i Niezawodność

Rocznik

2024

Tom

Vol. 26, no. 3

Strony

art. no. 187158

Opis fizyczny

Bibliogr. 56 poz., tab., wykr.

Twórcy

autor

Hasaballah Mustafa M.

mustafamath7@yahoo.com

Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt, Egypt

https://orcid.org/0000-0001-7680-6762

autor

Tashkandy Yusra A.

ytashkandi@ksu.edu.sa

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

https://orcid.org/0000-0003-2878-4460

autor

Balogun Oluwafemi Samsin

samson.balogun@uef.fi

Department of Computing, University of Eastern Finland, FI-70211, Finland, Finland

https://orcid.org/0000-0002-8870-9692

autor

Bakr M. E.

mmibrahim@ksu.edu.sa

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

https://orcid.org/0000-0003-3493-+033X

Bibliografia

1. Abbas S, Cakmakyapan S, Mustafa F, Ozel G, Shahbaz MQ. Extended Inverse Weibull Distribution with Application in Reliability Sciences. International Journal of Reliability, Quality and Safety Engineering 2023; 30(02). DOI: 10.1142/S0218539323500079
2. Abbas S, Taqi SA, Mustafa F, Murtaza M, Shahbaz MQ. Topp Leone inverse Weibull distribution: theory and application. European Journal of Pure and Applied Mathematics. 2017, 10(1), 1005–1022. https://ejpam.com/index.php/ejpam/article/view/3084
3. Abo-Kasem OE, Abdelgaffar A, Al Mutairi A, Khashab RH, Abu El Azm WS. Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application. AIP Advances 2023; 13 (11): 115-206. https://doi.org/10.1063/5.0174543
4. Abo-Kasem O.E, Abu El Fotouh S. and Khairy AA. Statistical analysis of inverse Weibull distribution based on generalized progressive hybrid type-I censoring with competing risks. Pakistan Journal of Statistics, 2024, 40(1):53-80.
5. Al-Essa LA, Soliman AA, Abd-Elmougod GA, Alshanbari HM. Adaptive Type-II Hybrid Progressive Censoring Samples for Statistical Inference of Comparative Inverse Weibull Distributions. Axioms. 2023; 12(10):973. https://doi.org/10.3390/axioms12100973
6. Alrashidi A., Rabie A., Mahmoud AA., Nasr SG., Mustafa MS., Al Mutairi A., Hussam E., Hossain MM. Exponentiated gamma constant-stress partially accelerated life tests with unified hybrid censored data: Statistical inferences. Alexandria Engineering Journal, 2024, 88, 268-275. https://doi.org/10.1016/j.aej.2023.12.066.
7. Aljeddani SM, Mohammed MA. An extensive mathematical approach for wind speed evaluation using inverse Weibull distribution. Alexandria Engineering Journal 2023; 76, 775-786, https://doi.org/10.1016/j.aej.2023.06.076.
8. Alshaikh, F. A.; Baklizi, A. Maximum Likelihood Estimation in the Inverse Weibull Distribution with Type II Censored Data, Mathematics and Statistics 2022; 10(6), 1304–1312, doi: 10.13189/ms.2022.100616.
9. Andrzejczak K, Bukowski L. A method for estimating the probability distribution of the lifetime for new technical equipment based on expert judgement. Eksploatacja i Niezawodność – Maintenance and Reliability. 2021; 23(4):757-769. doi:10.17531/ein.2021.4.18.
10. Ateya SF, Alghamdi AS, Mousa AAA. Future Failure Time Prediction Based on a Unified Hybrid Censoring Scheme for the Burr-X Model with Engineering Applications. Mathematics. 2022; 10(9):1450. https://doi.org/10.3390/math10091450
11. Asadi S, Panahi H, Anwar S, Lone SA. Reliability Estimation of Burr Type III Distribution under Improved Adaptive Progressive Censoring with Application to Surface Coating. Eksploatacja i Niezawodność – Maintenance and Reliability. 2023;25(2). doi:10.17531/ein/163054.
12. Balakrishnan N, Rasouli A, Farsipour NS. Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution. J Statist Comput Simulation. 2008 78(5), 475–488. DOI10.1080/00949650601158336
13. Basheer AM, Almetwally EM, Okasha HM. Marshall-Olkin alpha power inverse Weibull distribution: Non-Bayesian and Bayesian estimations. J. Stat. Appl. Probab. 2021; 10, 327–345. DOI: 10.18576/jsap/100205
14. Calabria R, Pulcini G. On the maximum likelihood and least-squares estimation in the inverse Weibull distributions. Statistica Applicata 1990; 2(1), 53–66.
15. Celik N, Guloksuz CT. A new lifetime distribution. Eksploatacja i Niezawodnosc - Maintenance and Reliability. 2017; 19 (4): 634-639, https://doi.org/10.17531/ein.2017.4.18.
16. Chandrasekar B, Childs A, Balakrishnan N. Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring. Nav Res Logist (NRL) 2004; 51(7), 994–1004. https://doi.org/10.1002/nav.20038
17. Chiou KC, Chen KS. Lifetime performance evaluation model based on quick response thinking. Eksploatacja i Niezawodnosc- Maintenance and Reliability 2022; 24 (1): 1-6, http://doi.org/10.17531/ein.2022.1.1.
18. Childs A, Chandrasekar B, Balakrishnan N, Kundu D. Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 2003; 55, 319–330. https://doi.org/10.1007/BF02530502
19. Dutta S, Kayal S. Bayesian and non-Bayesian inference of Weibull lifetime model based on partially observed competing risks data under unified hybrid censoring scheme. Qual Reliab Eng Int. 2022; 38: 3867–3891. https://doi.org/10.1002/qre.3180
20. Dutta S, Lio Y, Kayal S. Parametric inferences using dependent competing risks data with partially observed failure causes from MOBK distribution under unified hybrid censoring. Journal of Statistical Computation and Simulation. 2023; https://doi.org/10.1080/00949655.2023.2249165
21. Elshahhat A., Ahmad HH., Rabaiah A., Abo-Kasem OE. Analysis of a new jointly hybrid censored Rayleigh populations[J]. AIMS Mathematics, 2024, 9(2): 3740-3762. doi: 10.3934/math.2024184
22. Emam W, Sultan KS. Bayesian and maximum likelihood estimations of the Dagum parameters under combined-unified hybrid censoring. Mathematical Biosciences and Engineering 2021, 18(3): 2930-2951. doi: 10.3934/mbe.2021148.
23. Epstein B. Truncated Life Tests in the Exponential Case. Ann. Math. Statist. 25 (3) 555 - 564, 1954. https://doi.org/10.1214/aoms/1177728723
24. Ferreira LA, Silva JL. Parameter estimation for Weibull distribution with right censored data using EM algorithm. Eksploatacja i Niezawodnosc- Maintenance and Reliability 2017; 19 (2): 310-315, https://doi.org/10.17531/ein.2017.2.20.
25. Gusmao FRS, Ortega EMM, Cordeiro GM. The generalized inverse Weibull distribution. Statistical Papers 2011; 52, 591–619. https://doi.org/10.1007/s00362-009-0271-3
26. Hasaballah MM, Al-Babtain AA, Hossain MM, Bakr ME. Theoretical Aspects for Bayesian Predictions Based on Three-Parameter Burr-XII Distribution and Its Applications in Climatic Data. Symmetry. 2023; 15(8):1552. https://doi.org/10.3390/sym15081552
27. Hamdeni T, Gasmi S. The Marshall–Olkin generalized defective Gompertz distribution for surviving fraction modeling. Communications in Statistics-Simulation and Computation. 2020; p. 1–14. https://doi.org/10.1080/03610918.2020.1804937
28. Hassan MKH, Aslam M. DUS-neutrosophic multivariate inverse Weibull distribution: properties and applications. Complex Intell. Syst. 2023; https://doi.org/10.1007/s40747-023-01026-2.
29. Hussam E, Sabry MA, Abd El-Raouf MM, Almetwally EM. Fuzzy vs. Traditional Reliability Model for Inverse Weibull Distribution. Axioms. 2023; 12(6):582. https://doi.org/10.3390/axioms12060582
30. Ilori1 AK, Oladimeji DM. The Weighted Inverse Weibull Distribution. International Journal of Research and Innovation in Applied Science 2022; VII, Issue IV, DOI: 10.51584/IJRIAS.2022.7403
31. Jana, N.; Bera, S. Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model, Journal of Applied Statistics 2022; 49(1), 169–194, DOI: 10.1080/02664763.2020.1803815.
32. Jeon YE, Kang SB. Estimation of the Rayleigh Distribution under Unified Hybrid Censoring. Austrian Journal of Statistics 2021; 50(1), 59–73. https://doi.org/10.17713/ajs.v50i1.990
33. Jozani, JM, Marchand, É, Parsian A. Bayesian and Robust Bayesian analysis under a general class of balanced loss functions. Stat Papers 53, 51–60 (2012). https://doi.org/10.1007/s00362-010-0307-8
34. Khalaf AA., Yusur KA. and Khaleel MA. [0,1] Truncated Exponentiated Exponential Inverse Weibull Distribution with Applications of Carbon Fiber and COVID-19 Data, Al-Rafidain J Sci, vol. 54, no. 1, pp. 387–399, Jan. 2024, doi: 10.55562/jrucs.v54i1.608.
35. Keller AZ. Kanath ARR. Alternative reliability models for mechanical systems. Third International Conference on Reliability and Maintainability. Toulouse, France, 1982, 411–415.
36. Klakattawi HS. Survival analysis of cancer patients using a new extended Weibull distribution. PLoS ONE 2022; 17(2): e0264229. https://doi.org/10.1371/journal.pone.0264229
37. Lee ET, Wang JW. Statistical Methods for Survival Data Analysis. Third Edition, Wiley, New York. 2003; https://doi.org/10.1002/0471458546.
38. Lindley DV. Approximate Bayesian methods. Trabajos de Estadistica Y de Investigacion Operativa 1980; 31, 223–245. https://doi.org/10.1007/BF02888353
39. Lone SA., Panahi H. Estimation procedures for partially accelerated life test model based on unified hybrid censored sample from the Gompertz distribution. Eksploatacja i Niezawodnosc – Maintenance and Reliability 2022; 24 (3): 427–436, http://doi.org/10.17531/ ein.2022.3.4.
40. Lone SA., Panahi H. & Shah I. Bayesian prediction interval for a constant-stress partially accelerated life test model under censored data, Journal of Taibah University for Science, 2021, 15:1, 1178-1187, DOI: 10.1080/16583655.2021.2023847.
41. Lone SA., Rahman A. & slam A. Step stress partially accelerated life testing plan for competing risk using adaptive type-i progressive hybrid censoring, Pakistan Journal of Statistics. 2017, 33(4):237-248.
42. Muhammed HZ, Almetwally EM. Bayesian and non-Bayesian estimation for the bivariate inverse Weibull distribution under progressive type-II censoring. Ann. Data Sci. 2020; 10, 1–32. DOI: 10.1007/s40745-020-00316-7
43. Mahmoud, MR, Ismail AE, Ahmad MAM. Weibull-Inverse Exponential [Loglogistic] A New Distribution. Asian Journal of Probability and Statistics 2023; 21(3), 33–44. DOI:https://doi.org/10.9734/ajpas/2023/v21i3466.
44. Mahmoud, MAW, Sultan KS, Amer SM. Order statistics from inverse weibull distributionand associated inference. Computational Statistics & Data Analysis 2003; 42(1-2), 149-163. https://doi.org/10.1016/S0167-9473(02)00151-2
45. Nelson W. Applied Life Data Analysis. John Wiley and Sons, USA, 1982. DOI:10.1002/0471725234
46. Okasha, HM, Mohammed HS, Lio Y. E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications. Mathematics 2021; 9, 1261. https://doi.org/10.3390/math9111261
47. Panahi H, Sayyareh A. Estimation and prediction for a unified hybrid-censored Burr Type XII distribution. J Statist Comput Simulation. 2016; 86(1), 55–73. https://doi.org/10.1080/00949655.2014.993985
48. Rad AH, Izanlo M. An EM algorithm for estimating the parameters of the generalized exponential distribution under unified hybrid censored data. J Statist Res Iran JSRI. 2012; 8(2), 215–228. https://doi.org/10.18869/acadpub.jsri.8.2.215
49. Sarkar MH, Tripathy M. Estimating parameters of the inverse Gompertz distribution under unified hybrid censoring scheme. Palestine Journal of Mathematics 2022; 11(Special Issue III):172-188.
50. Sen T, Bhattacharya R, Pradhan B, Tripathi YM. Statistical inference and Bayesian optimal life-testing plans under Type-II unified hybrid censoring scheme. Qual Reliab Eng Int. 2021; 37(1), 78–89. DOI: 10.1007/s40745-018-0158-z
51. Shahbaz MQ, Saman S, Butt NS. The Kumaraswamy inverse Weibull distribution. Pakistan Journal of Statistics and Operation Research 2012; 3, 479–489. DOI:https://doi.org/10.18187/pjsor.v8i3.520
52. Shuaib MK, King R. New generalized inverse Weibull distribution for lifetime modeling. Communications for Statistical Applications and Methods. 2016; 3(2), 147–161. DOI: https://doi.org/10.5351/CSAM.2016.23.2.147.
53. Sindhu TN., Çolak AB., Lone SA., & Shafiq A. Reliability study of generalized exponential distribution based on inverse power law using artificial neural network with Bayesian regularization, Quality and Reliability Engineering International. 2023, https://doi.org/10.1002/qre.3352
54. Sultan KS, Emam W. The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties. Applied Sciences. 2021; 11(13):6000. https://doi.org/10.3390/app11136000
55. Yan Y, Zhou J, Yin Y, Nie H, Wei X, Liang T. Reliability Estimation of Retraction Mechanism Kinematic Accuracy under Small Sample. Eksploatacja i Niezawodność – Maintenance and Reliability. 2023. doi:10.17531/ein/174777.
56. Zellner, A. Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Association of Nurse Practitioners 1986; 81, 446–551, https://doi.org/10.1080/01621459.1986.10478289

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-305260c0-8280-4eef-b45d-400c0ceb419b