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Abdullah M, Ahsan-ul-Haq M, Alomair AM, Alomair MA. Classical and Bayesian inference for the new four-parameter Lomax distribution with applications. Heliyon 2024; 10:e25842. [PMID: 38384583 PMCID: PMC10878922 DOI: 10.1016/j.heliyon.2024.e25842] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Revised: 01/15/2024] [Accepted: 02/02/2024] [Indexed: 02/23/2024] Open
Abstract
In this study, a new four-parameter Lomax distribution is proposed using a new alpha power transformation technique. The new distribution is named "New Alpha Power Transformed Power Lomax Distribution." Mathematical properties, including moments, the moment-generating function, the mean residual life, order statistics, and the quantile function, are obtained. The maximum likelihood estimation approach is used to estimate the model parameters. A comprehensive simulation is used to evaluate the behavior of maximum likelihood estimators. Two real-world data sets were used to demonstrate the significance of the proposed model, and the results show that the new model performs better when interpreting lifetime data sets. In the end, for the data sets, Bayesian estimation and Metropolis-Hasting's approach were also utilized to construct the approximate Bayes estimates, and convergence diagnostic methods based on Markov Chain Monte Carlo techniques were applied.
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Affiliation(s)
| | | | - Abdullah M. Alomair
- Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
| | - Mohammed A. Alomair
- Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
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2
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Naveed M, Azam M, Khan N, Aslam M, Saleem M, Saeed M. Control chart for half normal and half exponential power distributed process. Sci Rep 2023; 13:8632. [PMID: 37244949 DOI: 10.1038/s41598-023-35884-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 05/25/2023] [Indexed: 05/29/2023] Open
Abstract
In this manuscript, we construct an attribute control chart (ACC) for the number of defective items using time-truncated life tests (TTLT) when the lifetime of a manufacturing item follows two lifetime data distributions: the half-normal distribution (HND) and the half-exponential power distribution (HEPD). To assess the potential of the proposed charts, necessary derivations are made to obtain the value of the average run length (ARL) when the production process is in-control and out-of-control. The performance of the presented charts is evaluated for different sample sizes, control coefficients, and truncated constants for shifted phases in terms of ARL. The behavior of ARLs is studied for the shifted process by introducing shifts in its parameters. The advantages of the proposed HEPD-based chart are discussed in the form of ARLs with HND and Exponential Distribution (ED) based ACCs under TTLT, showing the excellent assessment of the proposed chart. Additionally, the advantages of another proposed ACC using HND are compared with ED-based ACC, and the findings support the HND in the form of smaller ARLs. Finally, simulation testing and real-life implementation are also discussed for functional purposes.
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Affiliation(s)
- Muhammad Naveed
- Department of Statistics, National College of Business Administration and Economics, Lahore, 54660, Pakistan
- Department of Statistics, Govt Graduate College (B) Gulberg, Lahore, Pakistan
| | - Muhammad Azam
- Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, 54000, Pakistan
| | - Nasrullah Khan
- College of Statistical Science, University of the Punjab, Lahore, Pakistan
| | - Muhammad Aslam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia.
| | - Muhammad Saleem
- Department of Industrial Engineering, Faculty of Engineering-Rabigh, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
| | - Muhammad Saeed
- Department of Statistics, Minhaj University, Lahore, 54770, Pakistan
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On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications. Symmetry (Basel) 2022. [DOI: 10.3390/sym14050883] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.
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Abbas S, Mohsin M. On the Characteristics of the Pseudo-gamma Distribution with Application in Reliability and Medical Sciences. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY, TRANSACTIONS A: SCIENCE 2020. [DOI: 10.1007/s40995-020-00950-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Ahmad Z, Mahmoudi E, Hamedani GG, Kharazmi O. New methods to define heavy-tailed distributions with applications to insurance data. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1741942] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Zubair Ahmad
- Department of Statistics, Yazd University, Yazd, Iran
| | - Eisa Mahmoudi
- Department of Statistics, Yazd University, Yazd, Iran
| | - G. G. Hamedani
- Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI, USA
| | - Omid Kharazmi
- Department of Statistics, Faculty of Sciences, Vali-e-Asr university of Rafsanjan, Rafsanjan, Iran
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Eliwa MS, El-Morshedy M. Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1741919] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- M. S. Eliwa
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
| | - M. El-Morshedy
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- Department of Mathematics, College of Sciences and Humanities Studies in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
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Aslam M, Asghar Z, Hussain Z, Shah SF. A modified T-X family of distributions: classical and Bayesian analysis. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1732642] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Muhammad Aslam
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Zahid Asghar
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Zawar Hussain
- Department of Social and Allied Sciences, Cholistan University of Veterinary and Animal Sciences, Bahawalpur, Pakistan
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Afify AZ, Nassar M, Cordeiro GM, Kumar D. The Weibull Marshall–Olkin Lindley distribution: properties and estimation. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1715017] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Ahmed Z. Afify
- Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt
| | - Mazen Nassar
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudia Arabia
- Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, Egypt
| | - Gauss M. Cordeiro
- Departamento de Estatística, Universidade Federal de Pernambuco, Recife, Brazil
| | - Devendra Kumar
- Department of Statistics, Central University of Haryana, Mahendergarh, India
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Abbasi SA, Khaliq QUA, Omar MH, Riaz M. On designing a sequential based EWMA structure for efficient process monitoring. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2020. [DOI: 10.1080/16583655.2020.1712011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Saddam Akber Abbasi
- Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar
| | | | - M. Hafidz Omar
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
| | - Muhammad Riaz
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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Abbas N, Saeed U, Riaz M, Abbasi SA. On designing an assorted control charting approach to monitor process dispersion: an application to hard-bake process. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2019. [DOI: 10.1080/16583655.2019.1703481] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Nasir Abbas
- Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
| | - Usman Saeed
- Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
| | - Muhammad Riaz
- Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
| | - Saddam Akber Abbasi
- Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar
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