New Mellin-Based Estimation and GoF Criteria for the Beta-Weibull Model
Abstract In recent years, various probability distributions have been proposed for describing lifetime data. Such proposals are often made from a class of distributions and aim to gain flexibility to describe asymmetric and heavy tail patterns. The beta-G family proposed by Eugene et al. (Commun Sta...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2025-02-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/s44199-024-00100-z |
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| Summary: | Abstract In recent years, various probability distributions have been proposed for describing lifetime data. Such proposals are often made from a class of distributions and aim to gain flexibility to describe asymmetric and heavy tail patterns. The beta-G family proposed by Eugene et al. (Commun Stat Theory Methods 31:497–512. https://doi.org/10.1081/STA-120003130 , 2002) is one of most used classes. Even though this class and other competing proposals can provide distributions which are able even of characterizing multimodal data, efficient estimation methods for their parameters are mandatory. Works about new distributions often present maximum likelihood estimators (MLEs). In general, although their asymptotic properties are well-defined, MLEs do not always assume closed-form and require the use of interactive optimization sources. In this paper, we propose a new estimation method based on log-cumulant (LC) expressions for the beta-Weibull (BW) distribution, an important beta-G model. This process is called LC estimators (LCEs). Further, we furnish new BW goodness-of-fit measures to quantify the BW fits quality. Unlike MLEs, least squares estimators (LSEs), and weighted least squares estimators (WLSEs), our proposal depends only on solving one nonlinear equation. We perform Monte Carlo experiments to compare LCEs based on MLEs, LSEs, and WLSEs. Finally, we apply LCEs to real data. Results suggest our proposal may outperform the considered MLEs, LSEs, and WLSEs. |
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| ISSN: | 2214-1766 |