Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study
The type III discrete Weibull distribution can be used in reliability analysis for modeling failure data such as the number of shocks, cycles, or runs a component or a structure can overcome before failing. This paper describes three methods for estimating its parameters: two customary techniques an...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2013/946562 |
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| author | Alessandro Barbiero |
| author_facet | Alessandro Barbiero |
| author_sort | Alessandro Barbiero |
| collection | DOAJ |
| description | The type III discrete Weibull distribution can be used in reliability analysis for modeling failure data such as the number of shocks, cycles, or runs a component or a structure can overcome before failing. This paper describes three methods for estimating its parameters: two customary techniques and a technique particularly suitable for discrete distributions, which, in contrast to the two other techniques, provides analytical estimates, whose derivation is detailed here. The techniques’ peculiarities and practical limits are outlined. A Monte Carlo simulation study has been performed to assess the statistical performance of these methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Two applications of real data are provided with the aim of showing how the type III discrete Weibull distribution can fit real data, even better than other popular discrete models, and how the inferential procedures work. A software implementation of the model is also provided. |
| format | Article |
| id | doaj-art-cc3b4f30eb1a477cbfedfa9a6af68f86 |
| institution | OA Journals |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-cc3b4f30eb1a477cbfedfa9a6af68f862025-08-20T02:19:58ZengWileyJournal of Probability and Statistics1687-952X1687-95382013-01-01201310.1155/2013/946562946562Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative StudyAlessandro Barbiero0Department of Economics, Management and Quantitative Methods, Università degli Studi di Milano, Via Conservatorio, 7-20122 Milan, ItalyThe type III discrete Weibull distribution can be used in reliability analysis for modeling failure data such as the number of shocks, cycles, or runs a component or a structure can overcome before failing. This paper describes three methods for estimating its parameters: two customary techniques and a technique particularly suitable for discrete distributions, which, in contrast to the two other techniques, provides analytical estimates, whose derivation is detailed here. The techniques’ peculiarities and practical limits are outlined. A Monte Carlo simulation study has been performed to assess the statistical performance of these methods for different parameter combinations and sample sizes and then give some indication for their mindful use. Two applications of real data are provided with the aim of showing how the type III discrete Weibull distribution can fit real data, even better than other popular discrete models, and how the inferential procedures work. A software implementation of the model is also provided.http://dx.doi.org/10.1155/2013/946562 |
| spellingShingle | Alessandro Barbiero Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study Journal of Probability and Statistics |
| title | Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study |
| title_full | Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study |
| title_fullStr | Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study |
| title_full_unstemmed | Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study |
| title_short | Parameter Estimation for Type III Discrete Weibull Distribution: A Comparative Study |
| title_sort | parameter estimation for type iii discrete weibull distribution a comparative study |
| url | http://dx.doi.org/10.1155/2013/946562 |
| work_keys_str_mv | AT alessandrobarbiero parameterestimationfortypeiiidiscreteweibulldistributionacomparativestudy |