| Title:
|
Bayesian reference analysis for proportional hazards model of random censorship with Weibull distribution (English) |
| Author:
|
Ajmal, Maria |
| Author:
|
Danish, Muhammad Yameen |
| Author:
|
Tahira, Ayesha |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
25-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This article deals with the objective Bayesian analysis of random censorship model with informative censoring using Weibull distribution. The objective Bayesian analysis has a long history from Bayes and Laplace through Jeffreys and is reaching the level of sophistication gradually. The reference prior method of Bernardo is a nice attempt in this direction. The reference prior method is based on the Kullback-Leibler divergence between the prior and the corresponding posterior distribution and easy to implement when the information matrix exists in closed-form. We apply this method to Weibull random censorship model and compare it with Jeffreys and maximum likelihood methods. It is observed that the closed-form expressions for the Bayes estimators are not possible; we use importance sampling technique to obtain the approximate Bayes estimates. The behaviour of maximum likelihood and Bayes estimators is observed via extensive numerical simulation. The proposed methodology is used for the analysis of a real-life data for illustration and appropriateness of the model is tested by Henze goodness-of-fit test. (English) |
| Keyword:
|
Jeffreys prior method |
| Keyword:
|
reference prior method |
| Keyword:
|
random censorship model |
| Keyword:
|
Kaplan–Meier survival estimate |
| Keyword:
|
Henze goodness-of-fit test |
| MSC:
|
62F10 |
| MSC:
|
62F15 |
| MSC:
|
62N01 |
| MSC:
|
62N05 |
| idZBL:
|
Zbl 07511609 |
| idMR:
|
MR4405945 |
| DOI:
|
10.14736/kyb-2022-1-0025 |
| . |
| Date available:
|
2022-04-08T07:48:03Z |
| Last updated:
|
2022-08-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149600 |
| . |
| Reference:
|
[1] Abu-Taleb, A. A., Smadi, M. M., Alawneh, A. J.: Bayes estimation of the lifetime parameters for the exponential distribution..J. Math. Stat. 3 (2007), 106-108. MR 2405216, |
| Reference:
|
[2] Ajmal, M., Danish, M. Y., Tahira, A.: Objective Bayesian analysis for Weibull distribution with application to random censorship model..J. Stat. Comp. Sim. 92 (2022), 43-59. MR 4353144, |
| Reference:
|
[3] Berger, J. O., Bernardo, J. M.: Estimating a product of means: Bayesian analysis with reference priors..J. Am. Stat. Assoc. 84 (1989), 200-207. MR 0999679, |
| Reference:
|
[4] Berger, J. O., Bernardo, J. M.: Ordered group reference priors with applications to a multinomial problem..Biometrika 79 (1992), 25-37. MR 1158515, |
| Reference:
|
[5] Bernardo, J. M.: Reference posterior distributions for Bayesian inference (with discussion)..J. R. Stat. Soc. B 41 (1979), 113-147. MR 0547240 |
| Reference:
|
[6] Bernardo, J. M.: Bayesian Reference Analysis..A postgraduate tutorial course, Universitat de Valencia, Spain 1998. |
| Reference:
|
[7] Danish, M. Y., Aslam, M.: Bayesian inference for the randomly censored Weibull distribution..J. Stat. Comp. Sim. 84 (2014), 215-230. MR 3169322, |
| Reference:
|
[8] Danish, M. Y., Arshad, I. A., Aslam, M.: Bayesian inference for the randomly censored Burr type XII distribution..J. Appl. Stat. 45 (2018), 270-283. MR 3764726, |
| Reference:
|
[9] Fleming, T. R., Harrington, D. P.: Counting Processes and Survival Analysis..Wiley, New York 1990. Zbl 1079.62093, MR 1100924 |
| Reference:
|
[10] Garg, R., Dube, M., Kumar, K., Krishna, H.: On randomly censored generalized inverted exponential distribution..Am. J. Math. Manag. Sci. 35 (2016), 361-379. |
| Reference:
|
[11] Henze, N.: A quick omnibus test for the proportional hazards model of random censorship..Statistics 24 (1993), 253-263. MR 1240940, |
| Reference:
|
[12] Hollander, M., Proschan, F.: Testing to determine the underlying distribution using randomly censored data..Biometrics 35 (1979), 393-401. MR 0535776, |
| Reference:
|
[13] Hossain, A. M., Zimmer, W. J.: Comparison of estimation methods for Weibull parameters: complete and censored samples..J. Stat. Comp. Sim. 73 (2003), 145-153. MR 1963219, |
| Reference:
|
[14] Joarder, A., Krishna, H., Kundu, D.: Inference on Weibull parameters with conventional type I censoring..Comp. Stat. Data. Anal. 55 (2011), 1-11. MR 2736531, |
| Reference:
|
[15] Johnson, R., Kotz, S., Balakrishnan, N.: Continuous Univariate Distribution. Second edition..Wiley, New York 1995. MR 1299979 |
| Reference:
|
[16] Kaplan, E. L., Meier, P.: Nonparametric estimation from incomplete observations..J. Am. Stat. Assoc. 53 (1958), 457-481. Zbl 0089.14801, MR 0093867, |
| Reference:
|
[17] Kochar, S. C., Proschan, F.: Independence of time and cause of failure in the multiple dependent competing risks model..Statist. Sinica 1 (1991), 295-299. MR 1101328, |
| Reference:
|
[18] Koziol, J. A., Green, S. B.: A Cramer-von Mises statistic for randomly censored data..Biometrika 63 (1976), 465-474. MR 0448695, |
| Reference:
|
[19] Krishna, H., Vivekanand, Kumar, K.: Estimation in Maxwell distribution with randomly censored data..J. Stat. Comp. Sim. 85 (2015), 3560-3578. MR 3395684, |
| Reference:
|
[20] Kundu, D.: Bayesian inference and life testing plan for Weibull distribution in presence of progressive censoring..Technometrics 50 (2008), 144-154. MR 2439875, |
| Reference:
|
[21] Rinne, H.: The Weibull Distribution, A Handbook..CRC Press 2008. MR 2477856 |
| . |
