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Authors = Lishamol Tomy ORCID = 0000-0003-4092-6943

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24 pages, 515 KiB  
Article
Odd Exponential-Logarithmic Family of Distributions: Features and Modeling
by Christophe Chesneau, Lishamol Tomy, Meenu Jose and Kuttappan Vallikkattil Jayamol
Math. Comput. Appl. 2022, 27(4), 68; https://doi.org/10.3390/mca27040068 - 8 Aug 2022
Cited by 6 | Viewed by 2453
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models)
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16 pages, 444 KiB  
Article
Applications of the Sine Modified Lindley Distribution to Biomedical Data
by Lishamol Tomy, Veena G and Christophe Chesneau
Math. Comput. Appl. 2022, 27(3), 43; https://doi.org/10.3390/mca27030043 - 16 May 2022
Cited by 3 | Viewed by 2672
Abstract
In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth [...] Read more.
In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided. Full article
(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)
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15 pages, 468 KiB  
Article
The Sine Modified Lindley Distribution
by Lishamol Tomy, Veena G and Christophe Chesneau
Math. Comput. Appl. 2021, 26(4), 81; https://doi.org/10.3390/mca26040081 - 16 Dec 2021
Cited by 7 | Viewed by 2889
Abstract
The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. [...] Read more.
The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance. Full article
(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)
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31 pages, 745 KiB  
Review
Statistical Techniques for Environmental Sciences: A Review
by Lishamol Tomy, Christophe Chesneau and Amritha K. Madhav
Math. Comput. Appl. 2021, 26(4), 74; https://doi.org/10.3390/mca26040074 - 4 Nov 2021
Cited by 7 | Viewed by 15604
Abstract
This paper reviews the interdisciplinary collaboration between Environmental Sciences and Statistics. The usage of statistical methods as a problem-solving tool for handling environmental problems is the key element of this approach. This paper enhances a clear pavement for environmental scientists as well as [...] Read more.
This paper reviews the interdisciplinary collaboration between Environmental Sciences and Statistics. The usage of statistical methods as a problem-solving tool for handling environmental problems is the key element of this approach. This paper enhances a clear pavement for environmental scientists as well as quantitative researchers for their further collaborative learning with an analytical base. Full article
(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)
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