Type II general inverse exponential family of distributions

Jamal, Farrukh; Chesneau, Christophe; Elgarhy, Mohammed

doi:10.1080/09720510.2019.1668159

Cited by 18 publications

(15 citation statements)

References 14 publications

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“…The generated new distributions are more flexible in modelling data in practice. Some famous generators families are, Exponentiated -Weibull -generator (Elgarhy et al [2]), the Marshall-Olkin -G family by Marshal and Olkin [3], beta -G family by Eugene et al [4], the generalized odd log logistic -G by Cordeiro et al [5], the generalized transmuted-G by Nofal et al [6], the odd Lindley-G family by Gomes et al [7], a new extended alpha power transformed (APT)-G by Ahmad et al [8], a new APT-G by Elbatal et al [9], a new power Topp-Leone-G by Bantan et al [10], type II general inverse exponential-G by Jamal et al [11], Truncated Inverted Kumaraswamy-G by Bantan et al [12], the exponentiated truncated inverse Weibull-G by Almarashi et al [13], truncated Cauchy power-G by Aldahlan et al [14] and type II power Topp-Leone-G by Bantan et al [15], among others.…”

Section: Introductionmentioning

confidence: 99%

Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications

Elbatal¹,

Elgarhy²,

Kibria³

2021

JSTA

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This paper considers three special cases: Exponential, Rayleigh and Lindley of a family of generalized distributions, called alpha power Weibull G (APW-G) family. Some essential and valuable statistical properties of the family of distributions are obtained. The proposed distributions are very flexible and can be used to model data with decreasing, increasing or bathtub-shaped hazard rates. Model parameters estimation and a simulation study is carried out to evaluate the behaviors of the parameters. We consider two worthwhile data sets to illustrate the finding of the paper.

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Section: Introductionmentioning

confidence: 99%

Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications

Elbatal¹,

Elgarhy²,

Kibria³

2021

JSTA

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“…Then, the possible values of the new parameter(s) can significantly improve the statistical capabilities of the parent distribution, positively affecting the central and dispersion parameters, asymmetry, kurtosis and weight on the tails. Examples of such families are the exp-G family [35], Weibull-G family [20], Topp-Leone generated (TL-G) family [11], a new extended alpha power transformed-G [6], a new alpha power transformed-G [29], new power TL-G [17], type II general inverse exponential-G [40], truncated inverted Kumaraswamy-G [16], exponentiated truncated inverse Weibull-G [14], odd generalized NH-G [5], type II power TL-G [18] and others.…”

Section: Introductionmentioning

confidence: 99%

Sine Topp-Leone-G family of distributions: Theory and applications

et al. 2020

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Recent studies have highlighted the statistical relevance and applicability of trigonometric distributions for the modeling of various phenomena. This paper contributes to the subject by investigating a new trigonometric family of distributions defined from the alliance of the families known as sine-G and Topp-Leone generated (TL-G), inspiring the name of sine TL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Stochastic ordering and equivalence results, determination of the mode(s), some expansions of distributional functions, expressions of the quantile function and moments and basics on order statistics are discussed. In addition, we emphasize the fact that the sine TL-G family is able to generate original, simple and pliant trigonometric models for statistical purposes, beyond the capacity of the former sine-G models and other top models of the literature. This fact is revealed with the special three-parameter sine TL-G model based on the inverse Lomax model, through an efficient parametric estimation and the adjustment of two data sets of interest.

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“…For further detail on the inverse distributions, the reader is referred to [10][11][12]. Furthermore, several authors used the benefits of these inverse distributions for further perspectves, as the creation of general families of distributions, such as the inverse Weibull-G (IW-G) family by [13], type II general inverse exponential (TIIGIE) family by [14], generalized inverted Kumaraswamy-G (GIK-G) family by [15] and the generalized inverse Weibull-G (GIW-G) family by [16]. All these references demonstrate the success of the "inverse families" in many real-life applications dealing with data presenting various features (in terms of supports, skewness, kurtosis, uni/bimodal nature.…”

Section: Introductionmentioning

confidence: 99%

The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

Almarashi

Elgarhy

Jamal³

et al. 2020

Symmetry

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In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoretical and practical gains, both consequences of new flexible symmetric/asymmetric properties in a wide sense. Our main mathematical results are about stochastic ordering, uni/multimodality analysis, series expansions of crucial probability functions, probability weighted moments, raw and central moments, order statistics, and the maximum likelihood method. The special member of the family defined with the inverse Weibull distribution as baseline is highlighted. It constitutes a new four-parameter lifetime distribution which brightensby the multitude of different shapes of the corresponding probability density and hazard rate functions. Then, we use it for modelling purposes. In particular, a complete numerical study is performed, showing the efficiency of the corresponding maximum likelihood estimates by simulation work, and fitting three practical data sets, with fair comparison to six notable models of the literature.

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Type II general inverse exponential family of distributions

Cited by 18 publications

References 14 publications

Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications

Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications

Sine Topp-Leone-G family of distributions: Theory and applications

The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

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