Journal of the Iranian Statistical Society

Analysis of Dependent Competing Risk Model in the Presence of Joint Type-II Censoring Using Bivariate Marshll-Olkin Family

Document Type : Original Article

Authors

Department of Statistics, Faculty of Economics and Political Science, Cairo University, Egypt.

Abstract

Lifetime data has several applications in different fields such as Biology and Engineering. Failures for this type of data may occur due to several causes. In real world, causes of failures are interacting together which violates the independency assumption. Once dependency between failures is satisfied, bivariate families should be used to analyze the data. In literature, the majority of studies handle the case when data come from one source. However, in real life, data could come from different sources. One way to analyze data from different sources together and reduce the time and cost of the experiment is joint type-II censoring. To the best of our knowledge, joint type-II censoring was not yet derived using bivariate lifetime distributions. In this paper, we derive the likelihood function of joint type-II censoring using bivariate family in the presence of dependent competing risks. A simulation study is performed and two real datasets are analyzed.

Keywords

Abu-Zinadah, H. H. (2017), Statistical inferences with jointly type-II censored samples from two Pareto distributions. Open Physics. 15, 557-565.
Andrews, D. A., and Herzberg, A. M., (1985), Data: a Collection of Problems from Many Fields for the Student and Research Worker, Springer Series in Statistics, New York: Springer-Verlag.
Ashour and Abo-Kasem (2014), Parameter Estimation for two Weibull Populations under Joint Type II Censored Scheme. International Journal of Engineering and Applied Sciences. 5(4), 31-36.
Aly, H. M., and Abuelamayem, O. A. (2020), Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation. Mathematical Problems in Engineering. vol. 2020. https://doi.org/10.1155/2020/6349523.
Aly, H. M., and Abuelamayem, O. A. (2022), Generalization of the Ratio of Minimized KullbackLeibler Divergence Discrimination Technique to Bivariate Marshall-Olkin Family.Journal of Statistics Applications and Probability. 11(1), 57-73.
Bai, X. et al (2020), Inference of accelerated dependent competing risks model for Marshall-Olkin bivariate Weibull distribution with nonconstant parameters. Journal of Computational and Applied Mathematics. 336.
Balakrishnan, N. and Rasouli, A. (2008), Exact likelihood inference for two exponential populations under joint Type-II censoring. Computational Statistics and Data Analysis. 52(5), 2725-2738.
Balakrishnan, N., and Su, F. (2015), Exact Likelihood Inference for k Exponential Populations Under Joint Type-II Censoring. Communications in Statistics - Simulation and Computation. 44(3), 591-613.
Byrd, R. H., Lu, P., Nocedal, J., and Zhu, C. (1995), A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing. 16, 1190-1208.
Feizjavadian, S. H., and Hashemi, R. (2015), Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall-Olkin bivariateWeibull distribution. Computational Statistics and Data Analysis. 82, 19-34.
Kundu, D., and Sarhan, A. M. (2006), Analysis of Incomplete Data in Presence of Competing Risks Among Several Groups. IEEE Transactions on Reliability. 55(2), 262-269.
Kundu, D., and Gupta, R. D. (2009), "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, 100(4), 581-593.
Marshall, A.W. and Olkin, I. (1967), A multivariate exponential distribution. Journal of the American Statistical Association. 62(317), 30-44.
Mazucheli, J., and Achcar, J. A. (2011), The Lindley distribution applied to competing risks lifetime data.Computer Methods and Programs in Biomdicine. 104(2), 188-192.
Sarhan, A. M. (2007), Analysis of Incomplete, Censored Data in Competing Risks ModelsWith Generalized Exponential Distributions. IEEE Transactions on Reliability. 56(1), 132-138.
Sarhan, A. M. et al (2010), Statistical analysis of competing risks models. Reliability Engineering and System Safety. 95(9), 953–962.
Shen, Y., and Xu, A. (2018), On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with di erent methods. Communications in Statistics - Theory and Methods. 47(22), 5558-5572.
Wang, L., Li, M., and Tripathi, Y. M. (2020), Inference for dependent competing risks from bivariate Kumaraswamy distribution under generalized progressive hybrid censoring. Communications in Statistics - Simulation and Computation,1-24.
Journal of the Iranian Statistical Society
Volume 21, Issue 1
June 2022
Pages 127-151
  • Receive Date: 17 May 2021
  • Revise Date: 02 February 2022
  • Accept Date: 21 April 2022