The Fréchet Topp Leone-G Family of Distributions: Properties, Characterizations and Applications

Reyad, Hesham; Korkmaz, Mustafa Ç.; Afify, Ahmed Z.; Hamedani, G. G.; Othman, Soha

doi:10.1007/s40745-019-00212-9

Cited by 40 publications

(29 citation statements)

References 21 publications

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“…Using the same approach used to expand the PDF of EF-G, we apply the expansion in (11) and (12) to the PDF of EF-G in (4), that is,…”

Section: Rényi Entropymentioning

confidence: 99%

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The Exponentiated Fréchet Generator of Distributions with Applications

Baharith¹,

Alamoudi²

2021

Symmetry

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In this article, we introduce the exponentiated Fréchet-G family of distributions. Several models of the introduced exponentiated Fréchet-G family are presented. The proposed family is precisely more flexible and effective in modeling complex data and is instrumental in reliability analysis. It covers a wide variety of shapes, such as unimodal, reverse J, right-skewed, symmetrical, and asymmetrical shapes. Various structural mathematical properties, such as the quantile, moment, incomplete moment, entropy, and order statistics, are derived. The parameters are evaluated using a parametric estimation method. The performance and flexibility of the exponentiated Fréchet-G family are analyzed via a simulation and two applications; one deals with reliability data, and the other deals with medical data.

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“…Using the same approach used to expand the PDF of EF-G, we apply the expansion in (11) and (12) to the PDF of EF-G in (4), that is,…”

Section: Rényi Entropymentioning

confidence: 99%

“…Recently, new families have been introduced in the literature: the odd Fréchet-G [9], extended odd Fréchet-G [10], Fréchet Topp Leone-G [11], type II power Topp-Leone by [12], and exponentiated truncated inverse Weibull-G by [13].…”

Section: Introductionmentioning

confidence: 99%

The Exponentiated Fréchet Generator of Distributions with Applications

Baharith¹,

Alamoudi²

2021

Symmetry

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“…The second data set The second data set consists of 179 values of successive failure of the air conditioning system. For the data and more detail, we refer the reader to [24,25].…”

Section: Applicationsmentioning

confidence: 99%

Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

Bantan

Jamal²,

Chesneau

et al. 2019

Entropy

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In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature.

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“…On the other side, in the recent years, the Topp-Leone distribution reveals to be particularly efficient to define general families of distributions enjoying nice properties, including a great ability to model different practical data sets. Among these families, there are the Topp-Leone-G family studied via different approaches by [11][12][13][14], the Topp-Leone-G power series family by [15,16], the type II Topp-Leone-G family by [17], the Topp-Leone odd log-logistic family by [18], the type II generalized Topp-Leone-G family by [19], the Fréchet Topp-Leone-G family by [20], the exponentiated generalized Topp-Leone-G family by [21] and the transmuted Topp-Leone-G family by [22]. Now, for the purposes of this paper, let us describe the general family introduced by [23].…”

Section: Introductionmentioning

confidence: 99%

Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

Bantan

Jamal²,

Chesneau

et al. 2020

Symmetry

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In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

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The Fréchet Topp Leone-G Family of Distributions: Properties, Characterizations and Applications

Cited by 40 publications

References 21 publications

The Exponentiated Fréchet Generator of Distributions with Applications

The Exponentiated Fréchet Generator of Distributions with Applications

Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

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