Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis
The Lomax distribution has important applications in survival analysis, reliability engineering, insurance, finance, and other fields. Middle-censoring is an important censoring scheme, and data with middle-censoring will produce censoring in random intervals. This paper studies the parameter estima...
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MDPI AG
2025-04-01
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| author | Peiyao Ren Wenhao Gui Shan Liang |
| author_facet | Peiyao Ren Wenhao Gui Shan Liang |
| author_sort | Peiyao Ren |
| collection | DOAJ |
| description | The Lomax distribution has important applications in survival analysis, reliability engineering, insurance, finance, and other fields. Middle-censoring is an important censoring scheme, and data with middle-censoring will produce censoring in random intervals. This paper studies the parameter estimation of the Lomax distribution based on middle-censored data. The expectation–maximization algorithm is employed to compute the maximum likelihood estimates of the two unknown parameters of the Lomax distribution. After processing the data using the midpoint approach estimation, the parameter estimates are obtained by two computational methods: the Newton–Raphson iteration method and the fixed-point method. Moreover, the calculation methods for the asymptotic confidence intervals of the two parameters are provided, with the confidence interval coverage rate serving as one of the criteria for evaluating the estimation performance. In the Bayesian estimation aspect, the shape parameter is estimated using a Gamma prior distribution, and the Gibbs sampling method is employed for the solution. Finally, both simulation data and real data are used to compare the accuracy of the various estimation methods. |
| format | Article |
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| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-b694464af93b4d4f94864bf62c8f79682025-08-20T01:56:17ZengMDPI AGAxioms2075-16802025-04-0114533010.3390/axioms14050330Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative AnalysisPeiyao Ren0Wenhao Gui1Shan Liang2School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaSchool of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, ChinaThe Lomax distribution has important applications in survival analysis, reliability engineering, insurance, finance, and other fields. Middle-censoring is an important censoring scheme, and data with middle-censoring will produce censoring in random intervals. This paper studies the parameter estimation of the Lomax distribution based on middle-censored data. The expectation–maximization algorithm is employed to compute the maximum likelihood estimates of the two unknown parameters of the Lomax distribution. After processing the data using the midpoint approach estimation, the parameter estimates are obtained by two computational methods: the Newton–Raphson iteration method and the fixed-point method. Moreover, the calculation methods for the asymptotic confidence intervals of the two parameters are provided, with the confidence interval coverage rate serving as one of the criteria for evaluating the estimation performance. In the Bayesian estimation aspect, the shape parameter is estimated using a Gamma prior distribution, and the Gibbs sampling method is employed for the solution. Finally, both simulation data and real data are used to compare the accuracy of the various estimation methods.https://www.mdpi.com/2075-1680/14/5/330Lomax life distributionmiddle-censoringBayesian estimationEM algorithmMPA estimationGibbs sampling |
| spellingShingle | Peiyao Ren Wenhao Gui Shan Liang Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis Axioms Lomax life distribution middle-censoring Bayesian estimation EM algorithm MPA estimation Gibbs sampling |
| title | Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis |
| title_full | Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis |
| title_fullStr | Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis |
| title_full_unstemmed | Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis |
| title_short | Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis |
| title_sort | parameter estimation of the lomax lifetime distribution based on middle censored data methodology applications and comparative analysis |
| topic | Lomax life distribution middle-censoring Bayesian estimation EM algorithm MPA estimation Gibbs sampling |
| url | https://www.mdpi.com/2075-1680/14/5/330 |
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