Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications
We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernel...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/908 |
| _version_ | 1797533415415742464 |
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| author | Perla Celis Rolando de la Cruz Claudio Fuentes Héctor W. Gómez |
| author_facet | Perla Celis Rolando de la Cruz Claudio Fuentes Héctor W. Gómez |
| author_sort | Perla Celis |
| collection | DOAJ |
| description | We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution. |
| first_indexed | 2024-03-10T11:14:17Z |
| format | Article |
| id | doaj.art-7b6d247469d849ccb51a4c6d8321b2c4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:14:17Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7b6d247469d849ccb51a4c6d8321b2c42023-11-21T20:32:14ZengMDPI AGSymmetry2073-89942021-05-0113590810.3390/sym13050908Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with ApplicationsPerla Celis0Rolando de la Cruz1Claudio Fuentes2Héctor W. Gómez3Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Diagonal Las Torres 2640, Peñalolén, Santiago 7941169, ChileFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Diagonal Las Torres 2640, Peñalolén, Santiago 7941169, ChileDepartment of Statistics, Oregon State University, 217 Weniger Hall, Corvallis, OR 97331, USADepartamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileWe introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.https://www.mdpi.com/2073-8994/13/5/908censored dataEM algorithmepsilon–exponential distributionexponential distributionmaximum likelihoodreliability analysis |
| spellingShingle | Perla Celis Rolando de la Cruz Claudio Fuentes Héctor W. Gómez Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications Symmetry censored data EM algorithm epsilon–exponential distribution exponential distribution maximum likelihood reliability analysis |
| title | Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications |
| title_full | Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications |
| title_fullStr | Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications |
| title_full_unstemmed | Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications |
| title_short | Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications |
| title_sort | survival and reliability analysis with an epsilon positive family of distributions with applications |
| topic | censored data EM algorithm epsilon–exponential distribution exponential distribution maximum likelihood reliability analysis |
| url | https://www.mdpi.com/2073-8994/13/5/908 |
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