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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Main Authors: Peiyao Ren, Wenhao Gui, Shan Liang
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/5/330
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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.
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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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AT wenhaogui parameterestimationofthelomaxlifetimedistributionbasedonmiddlecensoreddatamethodologyapplicationsandcomparativeanalysis
AT shanliang parameterestimationofthelomaxlifetimedistributionbasedonmiddlecensoreddatamethodologyapplicationsandcomparativeanalysis