On a new modeling strategy: The logarithmically-exponential class of distributions

Abdulhakim A. Al-Babtain; Ibrahim Elbatal; Christophe Chesneau; Mohammed Elgarhy; Abdulhakim A. Al-Babtain; Ibrahim Elbatal; Christophe Chesneau; Mohammed Elgarhy

doi:10.3934/math.2021456

AIMS Mathematics

2021, Volume 6, Issue 7: 7845-7871. doi: 10.3934/math.2021456

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Research article

On a new modeling strategy: The logarithmically-exponential class of distributions

1.
Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
LMNO, Université de Caen Normandie, Campus II, Science 3, Caen 14032, France
4.
The Higher Institute of Commercial Sciences, Al mahalla Al kubra, Algarbia 31951, Egypt

Received: 28 January 2021 Accepted: 07 May 2021 Published: 18 May 2021
MSC : 60E05, 62E15, 62F30

In this paper, a promising modeling strategy for data fitting is derived from a new general class of univariate continuous distributions. This class is governed by an original logarithmically-exponential one-parameter transformation which has the ability to enhance some modeling capabilities of any parental distribution. In relation to the current literature, it appears to be a "limit case" of the well-established truncated generalized Fréchet generated class. In addition, it offers a natural alternative to the famous odd inverse exponential generated class. Some special distributions are presented, with particular interest in a novel heavy-tailed three-parameter distribution based on the Lomax distribution. Functional equivalences, modes analysis, stochastic ordering, functional expansions, moment measures, information measures and reliability measures are derived. From generic or real data, our modeling strategy is based on the new class combined with the maximum likelihood approach. We apply this strategy to the introduced modified Lomax model. The efficiency of the three parameter estimates is validated by a simulation study. Subsequently, two referenced real data sets are adjusted according to the rules of the art; the first one containing environmental data and the second one, financial data. In particular, we show that the proposed model is preferable to four concurrents also derived from the Lomax model, including the odd inverse exponential Lomax model.
- probability distribution theory,
- Lomax distribution,
- information measures,
- reliability measures,
- parametric estimation,
- simulation,
- data fitting
Citation: Abdulhakim A. Al-Babtain, Ibrahim Elbatal, Christophe Chesneau, Mohammed Elgarhy. On a new modeling strategy: The logarithmically-exponential class of distributions[J]. AIMS Mathematics, 2021, 6(7): 7845-7871. doi: 10.3934/math.2021456

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Abstract

In this paper, a promising modeling strategy for data fitting is derived from a new general class of univariate continuous distributions. This class is governed by an original logarithmically-exponential one-parameter transformation which has the ability to enhance some modeling capabilities of any parental distribution. In relation to the current literature, it appears to be a "limit case" of the well-established truncated generalized Fréchet generated class. In addition, it offers a natural alternative to the famous odd inverse exponential generated class. Some special distributions are presented, with particular interest in a novel heavy-tailed three-parameter distribution based on the Lomax distribution. Functional equivalences, modes analysis, stochastic ordering, functional expansions, moment measures, information measures and reliability measures are derived. From generic or real data, our modeling strategy is based on the new class combined with the maximum likelihood approach. We apply this strategy to the introduced modified Lomax model. The efficiency of the three parameter estimates is validated by a simulation study. Subsequently, two referenced real data sets are adjusted according to the rules of the art; the first one containing environmental data and the second one, financial data. In particular, we show that the proposed model is preferable to four concurrents also derived from the Lomax model, including the odd inverse exponential Lomax model.

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