1
|
Classical and Bayesian Inference Using Type-II Unified Progressive Hybrid Censored Samples for Pareto Model. Appl Bionics Biomech 2022; 2022:2073067. [PMID: 35528527 PMCID: PMC9076315 DOI: 10.1155/2022/2073067] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2022] [Revised: 02/17/2022] [Accepted: 03/08/2022] [Indexed: 11/18/2022] Open
Abstract
In the lifetime and reliability experiments, the censored samples play a fundamental and important role in order to control time and cost. The researchers developed the censored sample schemes to solve the problems that arise by applying the previous methods. Recently, Górny and Cramer (2018) proposed a new general type of censored sample called Type-II unified progressive hybrid censored sample. In this paper, we present an overview of the Type-II unified progressive hybrid censored sample. We used this censored sample to compute the maximum likelihood estimates of unknown parameters from the Pareto distribution, as well as Bayesian estimates for unknown parameters under three different error loss functions. The point and interval Bayesian predictions one- and two-sample Bayesian predictions from the Pareto distribution are shown. Simulation studies are carried out to compare the efficacy of the various inference approaches. Finally, real data sets are examined to determine the applicability of the proposed model and various estimating approaches.
Collapse
|
2
|
|
3
|
Saini S, Chaturvedi A, Garg R. Estimation of stress–strength reliability for generalized Maxwell failure distribution under progressive first failure censoring. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2020.1856846] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Shubham Saini
- Department of Statistics, University of Delhi, Delhi, India
| | | | - Renu Garg
- Department of Statistics, University of Delhi, Delhi, India
| |
Collapse
|
4
|
Inverse Maxwell Distribution and Statistical Process Control: An Efficient Approach for Monitoring Positively Skewed Process. Symmetry (Basel) 2021. [DOI: 10.3390/sym13020189] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
(1) Background: The literature discusses the inverse Maxwell distribution theoretically without application. Control charting is promising, but needs development for inverse Maxwell processes. (2) Methods: Thus, we develop the VIM control chart for monitoring the inverse Maxwell scale parameter and studied its statistical properties. The chart’s performance is evaluated using power curves and run length properties. (3) Results: Further, we use simulated data to compare the shift detection capability of our chart with Weibull, gamma, and lognormal charts. (4) Conclusion: The analysis demonstrates our chart’s efficiency for monitoring skewed processes. Finally, we apply our chart for monitoring real world lifetimes of car brake pads.
Collapse
|
5
|
Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2020. [DOI: 10.3390/mca25040065] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.
Collapse
|
6
|
A Review on Inverse Maxwell Distribution with Its Statistical Properties and Applications. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2020. [DOI: 10.1007/s42519-020-00100-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
7
|
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
|
8
|
Lodhi C, Mani Tripathi Y, Kumar Rastogi M. Estimating the parameters of a truncated normal distribution under progressive type II censoring. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1614619] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Chandrakant Lodhi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, Bihar, India
| | - Yogesh Mani Tripathi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, Bihar, India
| | | |
Collapse
|
9
|
Wang C, Liu H. Estimation for the scaled half-logistic distribution under Type-I progressively hybrid censoring scheme. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2017.1291968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Chao Wang
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P. R. China
| | - Hong Liu
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P. R. China
| |
Collapse
|
10
|
Chaudhary S, Kumar J, Tomer SK. Estimation of P[Y < X] for Maxwell distribution. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2017. [DOI: 10.1080/09720510.2017.1308064] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sachin Chaudhary
- Department of Statistics, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
| | - J. Kumar
- Department of Statistics, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
| | - Sanjeev K. Tomer
- Department of Statistics, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India
| |
Collapse
|
11
|
Saghir A, Khadim A, Lin Z. The Maxwell length-biased distribution: Properties and estimation. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2016. [DOI: 10.1080/15598608.2016.1246266] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Aamir Saghir
- Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
| | - Aneeqa Khadim
- Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur, Pakistan
| | - Zhengyan Lin
- Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou, P.R. China
| |
Collapse
|