A comparative study of bayesian and classical methods for the weighted Lindley distribution under unified hybrid censoring with survival data applications

Jiju Gillariose; Mahmoud M. Abdelwahab; Ibrahim Elbatal; Ninan P Oommen; Joshin Joseph; Mustafa M. Hasaballah; Jiju Gillariose; Mahmoud M. Abdelwahab; Ibrahim Elbatal; Ninan P Oommen; Joshin Joseph; Mustafa M. Hasaballah

doi:10.3934/math.2025987

AIMS Mathematics

2025, Volume 10, Issue 9: 22180-22205. doi: 10.3934/math.2025987

Previous Article Next Article

Research article Special Issues

A comparative study of bayesian and classical methods for the weighted Lindley distribution under unified hybrid censoring with survival data applications

1.
Department of Statistics and Data Science, Christ University, Hosur Road, Bangalore, Karnataka, 560029, India
2.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
SCAPS, Marian College Kuttikkanam, Kuttikkanam P.O, Peermade, Idukki District, Kerala, 685531, India
4.
Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo, 11721, Egypt

Received: 24 June 2025 Revised: 27 August 2025 Accepted: 18 September 2025 Published: 25 September 2025
MSC : 62G30, 62E10

In survival analysis and reliability engineering, censoring schemes play a crucial role in efficient data collection and analysis. This study investigated the unified hybrid censoring scheme (UHCS), a versatile framework that integrates multiple censoring strategies, to evaluate the suitability of the Weighted Lindley (WL) distribution for modeling lifetime data. Maximum likelihood estimates (MLEs) and their corresponding asymptotic confidence intervals are derived for the parameters of the WL distribution. In the Bayesian framework, parameter estimation was performed under a squared error loss function. A detailed Monte Carlo simulation study was conducted to compare the performance of classical and Bayesian estimators across various sample sizes and censoring schemes. The simulation results revealed that Bayesian estimators consistently yielded lower mean squared errors (MSEs) than their classical counterparts, and the associated credible intervals were generally narrower than the frequentist confidence intervals. To demonstrate the practical applicability of the proposed methods, the analysis was applied to real-world survival datasets. The results highlighted the effectiveness of the WL distribution under UHCS, offering valuable insights for researchers and practitioners in reliability and survival analysis.
- weighted Lindley distribution,
- unified hybrid censoring scheme,
- maximum likelihood estimation,
- Bayesian estimation,
- Markov Chain Monte Carlo,
- survival analysis,
- reliability modeling,
- censored data
Citation: Jiju Gillariose, Mahmoud M. Abdelwahab, Ibrahim Elbatal, Ninan P Oommen, Joshin Joseph, Mustafa M. Hasaballah. A comparative study of bayesian and classical methods for the weighted Lindley distribution under unified hybrid censoring with survival data applications[J]. AIMS Mathematics, 2025, 10(9): 22180-22205. doi: 10.3934/math.2025987

Related Papers:

Abstract

In survival analysis and reliability engineering, censoring schemes play a crucial role in efficient data collection and analysis. This study investigated the unified hybrid censoring scheme (UHCS), a versatile framework that integrates multiple censoring strategies, to evaluate the suitability of the Weighted Lindley (WL) distribution for modeling lifetime data. Maximum likelihood estimates (MLEs) and their corresponding asymptotic confidence intervals are derived for the parameters of the WL distribution. In the Bayesian framework, parameter estimation was performed under a squared error loss function. A detailed Monte Carlo simulation study was conducted to compare the performance of classical and Bayesian estimators across various sample sizes and censoring schemes. The simulation results revealed that Bayesian estimators consistently yielded lower mean squared errors (MSEs) than their classical counterparts, and the associated credible intervals were generally narrower than the frequentist confidence intervals. To demonstrate the practical applicability of the proposed methods, the analysis was applied to real-world survival datasets. The results highlighted the effectiveness of the WL distribution under UHCS, offering valuable insights for researchers and practitioners in reliability and survival analysis.

References

[1]	T. A. Abushal, Statistical inference for Nadarajah–Haghighi distribution under unified hybrid censored competing risks data, Heliyon, 10 (2024), e26794. http://dx.doi.org/10.1016/j.heliyon.2024.e26794 doi: 10.1016/j.heliyon.2024.e26794
[2]	A. Z. Afify, M. Nassar, G. M. Cordeiro, D. Kumar, The Weibull Marshall–Olkin Lindley distribution: Properties and estimation, J. Taibah Univ. Sci., 14 (2020), 192–204. http://dx.doi.org/10.1080/16583655.2020.1715017 doi: 10.1080/16583655.2020.1715017
[3]	N. Balakrishnan, A. Rasouli, N. S. Farsipour, Exact likelihood inference based on a unified hybrid censored sample from the exponential distribution, J. Stat. Comput. Sim., 78 (2008), 475–488. http://dx.doi.org/10.1080/00949650601158336 doi: 10.1080/00949650601158336
[4]	N. Balakrishnan, D. Kundu, Hybrid censoring: Models, inferential results and applications, Comput. Stat. Data An., 57 (2013), 166–209. http://dx.doi.org/10.1016/j.csda.2012.03.025 doi: 10.1016/j.csda.2012.03.025
[5]	B. Chandrasekar, A. Childs, N. Balakrishnan, Exact likelihood inference for the exponential distribution under generalized Type-Ⅰ and Type-Ⅱ hybrid censoring, Nav. Res. Log., 51 (2004), 994–1004. http://dx.doi.org/10.1002/nav.20038 doi: 10.1002/nav.20038
[6]	C. Chesneau, L. Tomy, J. Gillariose, On a sum and difference of two Lindley distributions: Theory and application, REVSTAT – Stat. J., 18 (2020), 673–695.
[7]	C. Chesneau, L. Tomy, J. Gillariose, F. Jamal, The inverted modified Lindley distribution, J. Stat. Theory Pract., 14 (2020), 46. http://dx.doi.org/10.1007/s42519-020-00116-5 doi: 10.1007/s42519-020-00116-5
[8]	C. Chesneau, L. Tomy, J. Gillariose, A new modified Lindley distribution with properties and applications, J. Stat. Manag. Syst., 24 (2021), 1383–1403.
[9]	A. Childs, B. Chandrasekar, N. Balakrishnan, D. Kundu, Exact likelihood inference based on Type-Ⅰ and Type-Ⅱ hybrid censored samples from the exponential distribution, Ann. I. Stat. Math., 55 (2003), 319–330. http://dx.doi.org/10.1007/BF02530502 doi: 10.1007/BF02530502
[10]	M. J. Cobo, A. G. López-Herrera, E. Herrera-Viedma, F. Herrera, Science mapping software tools: Review, analysis, and cooperative study among tools, J. Am. Soc. Inf. Sci. Tec., 62 (2011), 1382–1402. http://dx.doi.org/10.1002/asi.21525 doi: 10.1002/asi.21525
[11]	B. Efron, Logistic regression, survival analysis, and the Kaplan–Meier curve, J. Am. Stat. Assoc., 83 (1988), 414–425. http://dx.doi.org/10.1080/01621459.1988.10478612 doi: 10.1080/01621459.1988.10478612
[12]	B. Epstein, Truncated life tests in the exponential case, Ann. Math. Stat., 25 (1954), 555–564. http://dx.doi.org/10.1214/aoms/1177728723 doi: 10.1214/aoms/1177728723
[13]	M. E. Ghitany, B. Atieh, S. Nadarajah, Lindley distribution and its applications, Math. Comput. Simulat., 78 (2008), 493–506. http://dx.doi.org/10.1016/j.matcom.2007.06.007 doi: 10.1016/j.matcom.2007.06.007
[14]	Y. E. Jeon, S. B. Kang, Estimation of the Rayleigh distribution under unified hybrid censoring, Aust. J. Stat., 50 (2021), 59–73. http://dx.doi.org/10.17713/ajs.v50i1.990 doi: 10.17713/ajs.v50i1.990
[15]	H. Krishna, K. Kumar, Reliability estimation in Lindley distribution with progressive Type-Ⅱ right censored sample, Math. Comput. Simul., 82 (2011), 281–294. http://dx.doi.org/10.1016/j.matcom.2011.01.016 doi: 10.1016/j.matcom.2011.01.016
[16]	D. V. Lindley, Fiducial distributions and Bayes' theorem, J. Roy. Stat. Soc. B, 20 (1958), 102–107. http://dx.doi.org/10.1111/j.2517-6161.1958.tb00278.x doi: 10.1111/j.2517-6161.1958.tb00278.x
[17]	D. V. Lindley, Introduction to probability and statistics from a Bayesian viewpoint, Part Ⅱ: Inference, Cambridge University Press, New York, 1965.
[18]	J. Mazucheli, J. A. Achcar, The Lindley distribution applied to competing risks lifetime data, Comput. Meth. Prog. Bio., 104 (2011), 188–192. http://dx.doi.org/10.1016/j.cmpb.2011.03.006 doi: 10.1016/j.cmpb.2011.03.006
[19]	M. Nagy, A. F. Alrasheedi, Estimations of generalized exponential distribution parameters based on Type-Ⅰ generalized progressive hybrid censored data, Comput. Math. Method. M., 2022 (2022), 8058473. http://dx.doi.org/10.1155/2022/8058473 doi: 10.1155/2022/8058473
[20]	N. P. Oommen, J. Gillariose, Review of censoring schemes: Concepts, different types, model description, applications and future scope, Reliab. Theory Appl., 19 (2024), 287–300.
[21]	N. P. Oommen, J. Gillariose, Development and application of a new weighted Lindley distribution: Bayesian and Non-Bayesian estimation approaches [Preprint], 2025.
[22]	N. P. Oommen, J. Gillariose, Bayesian and non-bayesian inference of the generalized Lomax distribution under a unified hybrid censoring scheme with applications in failure times in biomedical and aerospace materials, Int. J. Syst. Assur. Eng., 2025. http://dx.doi.org/10.1007/s13198-025-02910-5
[23]	S. Park, N. Balakrishnan, A very flexible hybrid censoring scheme and its Fisher information, J. Stat. Comput. Simul., 82 (2012), 41–50. http://dx.doi.org/10.1080/00949655.2010.521503 doi: 10.1080/00949655.2010.521503
[24]	S. Polipu, J. Gillariose, Bayesian and Non-Bayesian parameter estimation for the bivariate odd Lindley Half-Logistic distribution using progressive type-Ⅱ censoring with applications in sports data, Modelling, 6 (2025), 13. http://dx.doi.org/10.3390/modelling6010013 doi: 10.3390/modelling6010013
[25]	D. A. Ramadan, Y. A. Tashkandy, O. S. Balogun, M. M. Hasaballah, Analysis of Marshall–Olkin extended Gumbel Type-Ⅱ distribution under progressive Type-Ⅱ censoring with applications, AIP Adv., 14 (2024), 055137. http://dx.doi.org/10.1063/5.0210905 doi: 10.1063/5.0210905
[26]	R. Shanker, F. Hagos, S. Sujatha, On modeling of lifetimes data using exponential and Lindley distributions, Biom. Biostat. Int. J., 2 (2015), 1–9.
[27]	K. S. Sultan, W. Emam, The combined-unified hybrid censored samples from Pareto distribution: Estimation and properties, Appl. Sci., 11 (2021), 6000. http://dx.doi.org/10.3390/app11136000 doi: 10.3390/app11136000
[28]	L. Tomy, J. Gillariose, A review on mathematically transformed Lindley random variables, Biom. Biostat. Int. J., 10 (2021), 46–48.
[29]	T. R. Tsai, Y. Lio, W. C. Ting, EM algorithm for mixture distributions model with Type-Ⅰ hybrid censoring scheme, Mathematics, 9 (2021), 2483. http://dx.doi.org/10.3390/math9192483 doi: 10.3390/math9192483

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)