Odd Exponential-Logarithmic Family of Distributions: Features and Modeling
This paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the “odd exponential logarithmic family”. We intend to create novel distributions with desired qualities for practical applications, using th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/27/4/68 |
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| author | Christophe Chesneau Lishamol Tomy Meenu Jose Kuttappan Vallikkattil Jayamol |
| author_facet | Christophe Chesneau Lishamol Tomy Meenu Jose Kuttappan Vallikkattil Jayamol |
| author_sort | Christophe Chesneau |
| collection | DOAJ |
| description | This paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the “odd exponential logarithmic family”. We intend to create novel distributions with desired qualities for practical applications, using the unique properties of the exponential-logarithmic distribution as an initial inspiration. Thus, we present some special members of this family that stand out for the versatile shape properties of their corresponding functions. Then, a comprehensive mathematical treatment of the family is provided, including some asymptotic properties, the determination of the quantile function, a useful sum expression of the probability density function, tractable series expressions for the moments, moment generating function, Rényi entropy and Shannon entropy, as well as results on order statistics and stochastic ordering. We estimate the model parameters quite efficiently by the method of maximum likelihood, with discussions on the observed information matrix and a complete simulation study. As a major interest, the odd exponential logarithmic models reveal how to successfully accommodate various kinds of data. This aspect is demonstrated by using three practical data sets, showing that an odd exponential logarithmic model outperforms two strong competitors in terms of data fitting. |
| first_indexed | 2024-03-09T04:07:55Z |
| format | Article |
| id | doaj.art-9d091b22ce6d45a9822eb5cb2e65091a |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T04:07:55Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-9d091b22ce6d45a9822eb5cb2e65091a2023-12-03T14:04:06ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472022-08-012746810.3390/mca27040068Odd Exponential-Logarithmic Family of Distributions: Features and ModelingChristophe Chesneau0Lishamol Tomy1Meenu Jose2Kuttappan Vallikkattil Jayamol3Department of Mathematics, LMNO, CNRS-Université de Caen, Campus II, Science 3, CEDEX, 14032 Caen, FranceDepartment of Statistics, Deva Matha College, Kuravilangad 686633, Kerala, IndiaDepartment of Statistics, Carmel College Mala, Thrissur 680732, Kerala, IndiaDepartment of Statistics, Maharajas College Ernakulam, Ernakulam 682011, Kerala, IndiaThis paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the “odd exponential logarithmic family”. We intend to create novel distributions with desired qualities for practical applications, using the unique properties of the exponential-logarithmic distribution as an initial inspiration. Thus, we present some special members of this family that stand out for the versatile shape properties of their corresponding functions. Then, a comprehensive mathematical treatment of the family is provided, including some asymptotic properties, the determination of the quantile function, a useful sum expression of the probability density function, tractable series expressions for the moments, moment generating function, Rényi entropy and Shannon entropy, as well as results on order statistics and stochastic ordering. We estimate the model parameters quite efficiently by the method of maximum likelihood, with discussions on the observed information matrix and a complete simulation study. As a major interest, the odd exponential logarithmic models reveal how to successfully accommodate various kinds of data. This aspect is demonstrated by using three practical data sets, showing that an odd exponential logarithmic model outperforms two strong competitors in terms of data fitting.https://www.mdpi.com/2297-8747/27/4/68exponential-logarithmic distributionT-X transformationmomentsentropymaximum likelihood estimationsimulation |
| spellingShingle | Christophe Chesneau Lishamol Tomy Meenu Jose Kuttappan Vallikkattil Jayamol Odd Exponential-Logarithmic Family of Distributions: Features and Modeling Mathematical and Computational Applications exponential-logarithmic distribution T-X transformation moments entropy maximum likelihood estimation simulation |
| title | Odd Exponential-Logarithmic Family of Distributions: Features and Modeling |
| title_full | Odd Exponential-Logarithmic Family of Distributions: Features and Modeling |
| title_fullStr | Odd Exponential-Logarithmic Family of Distributions: Features and Modeling |
| title_full_unstemmed | Odd Exponential-Logarithmic Family of Distributions: Features and Modeling |
| title_short | Odd Exponential-Logarithmic Family of Distributions: Features and Modeling |
| title_sort | odd exponential logarithmic family of distributions features and modeling |
| topic | exponential-logarithmic distribution T-X transformation moments entropy maximum likelihood estimation simulation |
| url | https://www.mdpi.com/2297-8747/27/4/68 |
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