1
|
Elshahhat A, Nassar M. Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models. Stat Pap (Berl) 2023. [DOI: 10.1007/s00362-023-01417-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2023]
Abstract
AbstractRecently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.
Collapse
|
2
|
Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data. MATHEMATICS 2022. [DOI: 10.3390/math10132258] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In reliability analysis and life testing studies, the experimenter is frequently interested in studying a specific risk factor in the presence of other factors. In this paper, the estimation of the unknown parameters, reliability and hazard functions of alpha power exponential distribution is considered based on progressively Type-II censored competing risks data. We assume that the latent cause of failures has independent alpha power exponential distributions with different scale and shape parameters. The maximum likelihood method is considered to estimate the model parameters as well as the reliability and hazard rate functions. The approximate and two parametric bootstrap confidence intervals of the different estimators are constructed. Moreover, the Bayesian estimation method of the unknown parameters, reliability and hazard rate functions are obtained based on the squared error loss function using independent gamma priors. To get the Bayesian estimates as well as the highest posterior credible intervals, the Markov Chain Monte Carlo procedure is implemented. A comprehensive simulation experiment is conducted to compare the performance of the proposed procedures. Finally, a real dataset for the relapse of multiple myeloma with transplant-related mortality is analyzed.
Collapse
|
3
|
Azm WSAE, Aldallal R, Aljohani HM, Nassr SG. Estimations of competing lifetime data from inverse Weibull distribution under adaptive progressively hybrid censored. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:6252-6275. [PMID: 35603400 DOI: 10.3934/mbe.2022292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In real-life experiments, collecting complete data is time-, finance-, and resources-consuming as stated by statisticians and analysts. Their goal was to compromise between the total time of testing, the number of units under scrutiny, and the expenditures paid through a censoring scheme. Comparing failure-censored schemes (Type-Ⅱ and Progressive Type-Ⅱ) to Time-censored schemes (Type-Ⅰ), it's worth noting that the former is time-consuming and is no more suitable to be applied in real-life situations. This is the reason why the Type-Ⅰ adaptive progressive hybrid censoring scheme has exceeded other failure-censored types; Time-censored types enable analysts to accomplish their trials and experiments in a shorter time and with higher efficiency. In this paper, the parameters of the inverse Weibull distribution are estimated under the Type-Ⅰ adaptive progressive hybrid censoring scheme (Type-Ⅰ APHCS) based on competing risks data. The model parameters are estimated using maximum likelihood estimation and Bayesian estimation methods. Further, we examine the asymptotic confidence intervals and bootstrap confidence intervals for the unknown model parameters. Monte Carlo simulations are carried out to compare the performance of the suggested estimation methods under Type-Ⅰ APHCS. Moreover, Markov Chain Monte Carlo by applying Metropolis-Hasting algorithm under the square error of loss function is used to compute Bayes estimates and related to the highest posterior density. Finally, two data sets are studied to illustrate the introduced methods of inference. Based on our results, we can conclude that the Bayesian estimation outperforms the maximum likelihood estimation for estimating the inverse Weibull parameters under Type-Ⅰ APHCS.
Collapse
Affiliation(s)
- Wael S Abu El Azm
- Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt
| | - Ramy Aldallal
- College of Business Administration in Hotat bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
| | - Hassan M Aljohani
- Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
| | - Said G Nassr
- Faculty of Business Administration, Sinai University, Al-Arish 45511, Egypt
| |
Collapse
|
4
|
Yadav CP, Tomer SK, Panwar MS. A competing risk study of menarcheal age distribution based on non-recall current status data. J Appl Stat 2022. [DOI: 10.1080/02664763.2022.2052821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- C. P. Yadav
- Department of Statistics, Banaras Hindu University, Varanasi, India
| | - Sanjeev K. Tomer
- Department of Statistics, Banaras Hindu University, Varanasi, India
| | - M. S. Panwar
- Department of Statistics, Banaras Hindu University, Varanasi, India
| |
Collapse
|
5
|
Bayesian Estimation Using Expected LINEX Loss Function: A Novel Approach with Applications. MATHEMATICS 2022. [DOI: 10.3390/math10030436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The loss function plays an important role in Bayesian analysis and decision theory. In this paper, a new Bayesian approach is introduced for parameter estimation under the asymmetric linear-exponential (LINEX) loss function. In order to provide a robust estimation and avoid making subjective choices, the proposed method assumes that the parameter of the LINEX loss function has a probability distribution. The Bayesian estimator is then obtained by taking the expectation of the common LINEX-based Bayesian estimator over the probability distribution. This alternative proposed method is applied to estimate the exponential parameter by considering three different distributions of the LINEX parameter, and the associated Bayes risks are also obtained in consequence. Extensive simulation studies are conducted in order to compare the performance of the proposed new estimators. In addition, three real data sets are analyzed to investigate the applicability of the proposed results. The results of the simulation and real data analysis show that the proposed estimation works satisfactorily and performs better than the conventional standard Bayesian approach in terms of minimum mean square error and Bayes risk.
Collapse
|
6
|
Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data. Symmetry (Basel) 2020. [DOI: 10.3390/sym12122005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.
Collapse
|
7
|
Ahmed EA, Ali Alhussain Z, Salah MM, Haj Ahmed H, Eliwa MS. Inference of progressively type-II censored competing risks data from Chen distribution with an application. J Appl Stat 2020; 47:2492-2524. [DOI: 10.1080/02664763.2020.1815670] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Essam A. Ahmed
- Department of Administrative and Financial Sciences, Taibah University, Community College of Khyber, Madinah, Saudi Arabia
- Mathematics Department, Sohag University, Sohag, Egypt
| | - Ziyad Ali Alhussain
- Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Majmaah, Saudi Arabia
| | - Mukhtar M. Salah
- Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Majmaah, Saudi Arabia
| | - Hanan Haj Ahmed
- Department of Basic Science, Preparatory Year Deanship, King Faisal University, Al-Ahsa, Saudi Arabia
| | - M. S. Eliwa
- Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Majmaah, Saudi Arabia
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
| |
Collapse
|
8
|
Okasha H, Mustafa A. E-Bayesian Estimation for the Weibull Distribution under Adaptive Type-I Progressive Hybrid Censored Competing Risks Data. ENTROPY 2020; 22:e22080903. [PMID: 33286672 PMCID: PMC7517528 DOI: 10.3390/e22080903] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 06/28/2020] [Revised: 08/13/2020] [Accepted: 08/13/2020] [Indexed: 11/16/2022]
Abstract
This article focuses on using E-Bayesian estimation for the Weibull distribution based on adaptive type-I progressive hybrid censored competing risks (AT-I PHCS). The case of Weibull distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E-Bayesian estimation is discussed by considering three different prior distributions for the hyper-parameters. The E-Bayesian estimators as well as the corresponding E-mean square errors are obtained by using squared and LINEX loss functions. Some properties of the E-Bayesian estimators are also derived. A simulation study to compare the various estimators and real data application is applied to show the applicability of the different estimators are proposed.
Collapse
Affiliation(s)
- Hassan Okasha
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
- Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt
- Correspondence:
| | - Abdelfattah Mustafa
- Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia;
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
| |
Collapse
|
9
|
Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring. Symmetry (Basel) 2020. [DOI: 10.3390/sym12071149] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.
Collapse
|
10
|
Bai X, Shi Y, Liu Y, Ng HKT, Liu B. Statistical analysis of competing risks model from Marshall–Olkin extended Chen distribution under adaptive progressively interval censoring with random removals. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2018.1481973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Xuchao Bai
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China
| | - Yimin Shi
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China
| | - Yiming Liu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China
| | - Hon Keung Tony Ng
- Department of Statistical Science, Southern Methodist University, Dallas, Texas, USA
| | - Bin Liu
- School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, China
| |
Collapse
|