1
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Abushal TA. Statistical inference for Nadarajah-Haghighi distribution under unified hybrid censored competing risks data. Heliyon 2024; 10:e26794. [PMID: 38562494 PMCID: PMC10982900 DOI: 10.1016/j.heliyon.2024.e26794] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Revised: 01/23/2024] [Accepted: 02/20/2024] [Indexed: 04/04/2024] Open
Abstract
Nadarajah and Haghighi distribution (NHD) inferences problem has been discussed under unified hybrid censoring scheme (UHCS) in the existence of competing risks model. Competing risks model is defined by time-to-failure under more than one cause of failure, which can be dependent or independent. This study focuses on discussing the case of failure partially observed causes of failure competing risks model. We obtain various inferences: we first obtain the MLE, in addition, we construct approximate confidence intervals (ACIs). Second, we obtain the Bayes estimator via SELF and related highest posterior density (HPD) using Markov Chain Monte Carlo (MCMC). Finally, an electrical appliances data set and simulation studies have been analyzed for further illustrations.
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Affiliation(s)
- Tahani A. Abushal
- Department of Mathematics, Faculty of Sciences, Umm AL-Qura University, Saudi Arabia
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2
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Aljohani HM. Estimation for the P( X > Y) of Lomax distribution under accelerated life tests. Heliyon 2024; 10:e25802. [PMID: 38371973 PMCID: PMC10873739 DOI: 10.1016/j.heliyon.2024.e25802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Revised: 01/06/2024] [Accepted: 02/02/2024] [Indexed: 02/20/2024] Open
Abstract
The system or unit survives when strength is more significant than the stress enjoined. This procedure is usually used in many companies to test their product. The reliability or the quality of the scheme or component is described by the parameters of stress-strength reliability (R = P ( X > Y )) where X denotes strength and Y indicates stress. In this article, we adopted the statistical inference of R while the two arbitrary factors X and Y are independent and approach the Lomax lifetime distribution with common scale parameters. Also, the strength and stress variables are subjected to a partial step-stress-quickened life experiment. The classical estimation and Bayes method create the point estimate of R. Confidence intervals of R are computed with asymptotic distribution, bootstrap technique, and Bayesian credible intervals. All results are evaluated and compared under an extensive simulation study. Finally, the lifetime data sets generated from the Lomax distribution are used to analyze the system's reliability by estimating R.
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Affiliation(s)
- Hassan M. Aljohani
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
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3
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Tolba AH, Muse AH, Fayomi A, Baaqeel HM, Almetwally EM. The Gull Alpha Power Lomax distributions: Properties, simulation, and applications to modeling COVID-19 mortality rates. PLoS One 2023; 18:e0283308. [PMID: 37676891 PMCID: PMC10484464 DOI: 10.1371/journal.pone.0283308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2022] [Accepted: 03/06/2023] [Indexed: 09/09/2023] Open
Abstract
The Gull Alpha Power Lomax distribution is a new extension of the Lomax distribution that we developed in this paper (GAPL). The proposed distribution's appropriateness stems from its usefulness to model both monotonic and non-monotonic hazard rate functions, which are widely used in reliability engineering and survival analysis. In addition to their special cases, many statistical features were determined. The maximum likelihood method is used to estimate the model's unknown parameters. Furthermore, the proposed distribution's usefulness is demonstrated using two medical data sets dealing with COVID-19 patients' mortality rates, as well as extensive simulated data applied to assess the performance of the estimators of the proposed distribution.
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Affiliation(s)
- Ahlam H. Tolba
- Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
| | - Abdisalam Hassan Muse
- Faculty of Science and Humanities, School of Postgraduate Studies and Research, Amoud University, Borama, Somalia
| | - Aisha Fayomi
- Faculty of Science Department of Statistics King Abdulaziz University, Jeddah, Saudi Arabia
| | - Hanan M. Baaqeel
- Faculty of Science Department of Statistics King Abdulaziz University, Jeddah, Saudi Arabia
| | - Ehab M. Almetwally
- Department of Statistics, Faculty of Business Administration, Delta University for Science and Technology, Gamasa, Egypt
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4
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Farghal AWA, Badr SK, Abu-Zinadah H, Abd-Elmougod GA. Analysis of generalized inverted exponential competing risks model in presence of partially observed failure modes. ALEXANDRIA ENGINEERING JOURNAL 2023; 78:74-87. [DOI: 10.1016/j.aej.2023.07.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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5
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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.
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6
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Abushal T, Soliman A, Abd-Elmougod G. Inference of partially observed causes for failure of Lomax competing risks model under type-II generalized hybrid censoring scheme. ALEXANDRIA ENGINEERING JOURNAL 2022; 61:5427-5439. [DOI: 10.1016/j.aej.2021.10.058] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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7
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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.
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8
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Burr XII Distribution for Disease Data Analysis in the Presence of a Partially Observed Failure Mode. Symmetry (Basel) 2022. [DOI: 10.3390/sym14071298] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
Modeling competing failure modes is an important problem in engineering and survival analyses. Competing failure modes are partially observed in many applications and often pose a modeling challenge. This study discusses the inference for partially observed failure modes assuming a Burr XII distribution. In particular, we consider two failure modes, and the failure time data are collected under a hybrid type I censoring scheme. The model parameters are estimated using maximum likelihood and Bayesian methods under a symmetric squared error loss function, whereas the intervals estimation is done with three methods: asymptotic and credible confidence intervals. Besides a simulation study, a real-life data set is taken from individuals who live in an environment with several diseases to present the utility of the work. Additionally, a simulation study is constructed to measure and compare different estimation methods.
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9
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Qin X, Gui W. Statistical inference of Lomax distribution based on adaptive progressive Type-II hybrid censored competing risks data. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2056750] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Xinyan Qin
- Department of Mathematics, Beijing Jiaotong University, Beijing, China
| | - Wenhao Gui
- Department of Mathematics, Beijing Jiaotong University, Beijing, China
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10
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Hua R, Gui W. Inference for copula-based dependent competing risks model with step-stress accelerated life test under generalized progressive hybrid censoring. Comput Stat 2022. [DOI: 10.1007/s00180-022-01203-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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11
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Lv Q, Hua R, Gui W. Statistical inference of Gompertz distribution under general progressive type II censored competing risks sample. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2028834] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Qi Lv
- Department of Mathematics, Beijing Jiaotong University, Beijing, China
| | - Rui Hua
- Department of Mathematics, Beijing Jiaotong University, Beijing, China
| | - Wenhao Gui
- Department of Mathematics, Beijing Jiaotong University, Beijing, China
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12
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Du Y, Gui W. Statistical inference of adaptive type II progressive hybrid censored data with dependent competing risks under bivariate exponential distribution. J Appl Stat 2021; 49:3120-3140. [DOI: 10.1080/02664763.2021.1937961] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Yuge Du
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
| | - Wenhao Gui
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
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13
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Tian Y, Gui W. Inference of weighted exponential distribution under progressively Type-II censored competing risks model with electrodes data. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1928128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Yajie Tian
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
| | - Wenhao Gui
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
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14
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Lodhi C, Tripathi YM, Wang L. Inference for a general family of inverted exponentiated distributions with partially observed competing risks under generalized progressive hybrid censoring. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1901290] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Chandrakant Lodhi
- neurIOT Technologies LPP, CoWorks, Golf, Course, Gurugram, Patna, India
| | | | - Liang Wang
- School of Mathematics, Yunnan Normal University, Kunming, People's Republic of China
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15
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Çetinkaya Ç. Reliability estimation of a stress-strength model with non-identical component strengths under generalized progressive hybrid censoring scheme. STATISTICS-ABINGDON 2021. [DOI: 10.1080/02331888.2021.1890739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Çağatay Çetinkaya
- Department of Business Administration, Faculty of Economics & Administrative Sciences Bingöl University, Bingöl, Turkey
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16
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Mahto AK, Lodhi C, Tripathi YM, Wang L. Inference for partially observed competing risks model for Kumaraswamy distribution under generalized progressive hybrid censoring. J Appl Stat 2021; 49:2064-2092. [DOI: 10.1080/02664763.2021.1889999] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | | | | | - Liang Wang
- School of Mathematics, Yunnan Normal University, Kunming, People's Republic of China
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17
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Lodhi C, Tripathi YM, Bhattacharya R. On a progressively censored competing risks data from Gompertz distribution. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1879141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Chandrakant Lodhi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, India
| | | | - Ritwik Bhattacharya
- Department of Industrial Engineering, School of Engineering and Sciences, Tecnológico de Monterrey, Querétaro, México
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18
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Amiri L, Ganjali M, Hashemi R, Khazaei M. The competing risks analysis for parallel and series systems using Type-II progressive censoring. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1620779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Leila Amiri
- Department of Statistics, Shahid Beheshti University, Tehran, Iran
| | - Mojtaba Ganjali
- Department of Statistics, Shahid Beheshti University, Tehran, Iran
| | - Reza Hashemi
- Department of Statistics, Razi University, Kermanshah, Iran
| | - Mojtaba Khazaei
- Department of Statistics, Shahid Beheshti University, Tehran, Iran
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19
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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
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20
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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.
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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
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21
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Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution. Comput Stat 2020. [DOI: 10.1007/s00180-020-01021-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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22
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Davies KF, Volterman W. Progressively Type-II censored competing risks data from the linear exponential distribution. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2020.1764044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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23
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Almarashi AM, Algarni A, Abd-Elmougod G. Statistical analysis of competing risks lifetime data from Nadarajaha and Haghighi distribution under type-II censoring. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-179546] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Abdullah M. Almarashi
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabi
| | - Ali Algarni
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabi
| | - G.A. Abd-Elmougod
- Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
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24
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Abu-Zinadah HH. Lifetime competing risks data from Lomax distribution in the presence of accelerates life-testing model with Type-I censoring. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-179573] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Hanaa H. Abu-Zinadah
- Department of Statistics, Faculty of Science, University ofJeddah, Jeddah, Saudi Arabia
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25
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Wang L, Li M, Tripathi YM. Inference for dependent competing risks from bivariate Kumaraswamy distribution under generalized progressive hybrid censoring. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2019.1708929] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Liang Wang
- School of Mathematics, Yunnan Normal University, Kunming, P.R. China
- School of Mathematics and Statistics, Xidian University, Xi’an, P.R. China
| | - Mengyang Li
- School of Mathematics and Statistics, Xidian University, Xi’an, P.R. China
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26
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Hu X, Gui W. Assessing the lifetime performance index with Lomax distribution based on progressive type I interval censored sample. J Appl Stat 2019; 47:1757-1775. [DOI: 10.1080/02664763.2019.1693523] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Xuehua Hu
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
| | - Wenhao Gui
- Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China
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27
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Statistical Inference of the Rayleigh Distribution Based on Progressively Type II Censored Competing Risks Data. Symmetry (Basel) 2019. [DOI: 10.3390/sym11070898] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
A competing risks model under progressively type II censored data following the Rayleigh distribution is considered. We establish the maximum likelihood estimation for unknown parameters and compute the observed information matrix and the expected Fisher information matrix to construct the asymptotic confidence intervals. Moreover, we obtain the Bayes estimation based on symmetric and non-symmetric loss functions, that is, the squared error loss function and the general entropy loss function, and the highest posterior density intervals are also derived. In addition, a simulation study is presented to assess the performances of different methods discussed in this paper. A real-life data set analysis is provided for illustration purposes.
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28
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Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals. Comput Stat 2018. [DOI: 10.1007/s00180-018-0847-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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29
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Liu F, Shi Y. Inference for a simple step-stress model with progressively censored competing risks data from Weibull distribution. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1147585] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Fen Liu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
| | - Yimin Shi
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
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30
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Affiliation(s)
- Fariba Hemmati
- Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
| | - Esmaile Khorram
- Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
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31
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Shi Y, Wu M. Statistical analysis of dependent competing risks model from Gompertz distribution under progressively hybrid censoring. SPRINGERPLUS 2016; 5:1745. [PMID: 27795888 PMCID: PMC5055528 DOI: 10.1186/s40064-016-3421-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/13/2015] [Accepted: 09/28/2016] [Indexed: 11/10/2022]
Abstract
Previous studies have mostly considered the competing risks to be independent even when the interpretation of the failure modes implies dependency. This paper studies the dependent competing risks model from Gompertz distribution under Type-I progressively hybrid censoring scheme. We derive the maximum likelihood estimations of the model parameters, and then the asymptotic likelihood theory and Bootstrap method are used to obtain the confidence intervals. The simulation results are provided to investigate the effects of different dependence structures on the estimations of parameters. Finally, one data set was used for illustrative purpose.
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Affiliation(s)
- Yimin Shi
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
| | - Min Wu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
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32
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Rady EHA, Hassanein WA, Elhaddad TA. The power Lomax distribution with an application to bladder cancer data. SPRINGERPLUS 2016; 5:1838. [PMID: 27818876 PMCID: PMC5074989 DOI: 10.1186/s40064-016-3464-y] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2016] [Accepted: 10/05/2016] [Indexed: 11/23/2022]
Abstract
A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data. POLO distribution accommodate both inverted bathtub and decreasing hazard rate. Several statistical and reliability properties are derived. Point estimation via method of moments and maximum likelihood and the interval estimation are also studied. The simulation schemes are calculated to examine the bias and mean square error of the maximum likelihood parameter estimators. Finally, a real data application about the remission time of bladder cancer is used to illustrate the usefulness of the proposed distribution in modelling real data application. The characteristics of the fitting data using the proposed distribution are compared with known extensions of Lomax distribution. The comparison showed that the POLO distribution outfit most well-known extensions of Lomax distribution.
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Affiliation(s)
| | | | - T A Elhaddad
- Faculty of Science, Tanta University, Tanta, Egypt
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33
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Wu M, Shi Y, Sun Y. Statistical analysis for competing risks model from a Weibull distribution under progressively hybrid censoring. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2014.985838] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Min Wu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
| | - Yimin Shi
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
| | - Yudong Sun
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
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Ahmadi K, Rezaei M, Yousefzadeh F. Point predictors of the latent failure times of censored units in progressively Type-II censored competing risks data from the exponential distributions. J STAT COMPUT SIM 2016. [DOI: 10.1080/00949655.2015.1079634] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Huang SR, Wu SJ. Optimal sample size allocation for accelerated life test under progressive type-II censoring with competing risks. J STAT COMPUT SIM 2016. [DOI: 10.1080/00949655.2016.1187608] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Syuan-Rong Huang
- Department of Statistics, Tamkang University, New Taipei City, Taiwan
| | - Shuo-Jye Wu
- Department of Statistics, Tamkang University, New Taipei City, Taiwan
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Ashour SK, Nassar M. Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2015.1083111] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Ahmadi K, Yousefzadeh F, Rezaei M. Analysis of progressively type-I interval censored competing risks data for a class of an exponential distribution. J STAT COMPUT SIM 2016. [DOI: 10.1080/00949655.2016.1178747] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Sun Y, Li M, Gilbert PB. Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark. Comput Stat Data Anal 2016; 93:348-358. [PMID: 26461462 DOI: 10.1016/j.csda.2014.11.012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Motivated by the need to assess HIV vaccine efficacy, previous studies proposed an extension of the discrete competing risks proportional hazards model, in which the cause of failure is replaced by a continuous mark only observed at the failure time. However the model assumptions may fail in several ways, and no diagnostic testing procedure for this situation has been proposed. A goodness-of-fit test procedure for the stratified mark-specific proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazards depends nonparametrically on both time and the mark is proposed. The test statistics are constructed based on the weighted cumulative mark-specific martingale residuals. The critical values of the proposed test statistics are approximated using the Gaussian multiplier method. The performance of the proposed tests are examined extensively in simulations for a variety of the models under the null hypothesis and under different types of alternative models. An analysis of the 'Step' HIV vaccine efficacy trial using the proposed method is presented. The analysis suggests that the HIV vaccine candidate may increase susceptibility to HIV acquisition.
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Affiliation(s)
- Yanqing Sun
- Department of Mathematics and Statistics University of North Carolina at Charlotte, Charlotte, NC 28223
| | - Mei Li
- School of Public Health Zhejiang University, Hangzhou, China
| | - Peter B Gilbert
- Department of Biostatistics, University of Washington and Fred Hutchinson Cancer Research Center, Seattle, WA 98109
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Helu A, Samawi H, Raqab MZ. Estimation on Lomax progressive censoring using the EM algorithm. J STAT COMPUT SIM 2013. [DOI: 10.1080/00949655.2013.861837] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Mao S, Shi YM, Sun YD. Exact inference for competing risks model with generalized type-I hybrid censored exponential data. J STAT COMPUT SIM 2013. [DOI: 10.1080/00949655.2013.851681] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Tian Y, Zhu Q, Tian M. Inference for mixed generalized exponential distribution under progressively type-II censored samples. J Appl Stat 2013. [DOI: 10.1080/02664763.2013.847070] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Giles DE, Feng H, Godwin RT. On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution. COMMUN STAT-THEOR M 2013. [DOI: 10.1080/03610926.2011.600506] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Progressively first-failure censored reliability sampling plans with cost constraint. Comput Stat Data Anal 2012. [DOI: 10.1016/j.csda.2011.12.008] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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