Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA

Hassan, Marwa K. H.; Chesneau, Christophe

doi:10.3390/mca27040072

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…The vector hazard rate function of BFGMPLx is obtained by substituting the above expressions in (25). Eq (27) consists of two terms: the first term…”

Section: Hazard Rate Functionmentioning

confidence: 99%

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Bivariate power Lomax distribution with medical applications

Qura

Fayomi

Kilai³

et al. 2023

PLoS ONE

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In this paper, a bivariate power Lomax distribution based on Farlie-Gumbel-Morgenstern (FGM) copulas and univariate power Lomax distribution is proposed, which is referred to as BFGMPLx. It is a significant lifetime distribution for modeling bivariate lifetime data. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, product moments, positive quadrant dependence property, and Pearson’s correlation, have been studied. The reliability measures, such as the survival function, hazard rate function, mean residual life function, and vitality function, have also been discussed. The parameters of the model can be estimated through maximum likelihood and Bayesian estimation. Additionally, asymptotic confidence intervals and credible intervals of Bayesian’s highest posterior density are computed for the parameter model. Monte Carlo simulation analysis is used to estimate both the maximum likelihood and Bayesian estimators.

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“…The vector hazard rate function of BFGMPLx is obtained by substituting the above expressions in (25). Eq (27) consists of two terms: the first term…”

Section: Hazard Rate Functionmentioning

confidence: 99%

“…Abulebda et al [26] introduced a new bivariate XGamma (BXG) distribution and investigated its statistical properties through examination of real data. Hassan et al [27] proposed the bivariate generalized half-logistic distribution using the FGM copula to asses household financial affordability in the Kingdom of Saudi Arabia.…”

Section: Introductionmentioning

confidence: 99%

Bivariate power Lomax distribution with medical applications

Qura

Fayomi

Kilai³

et al. 2023

PLoS ONE

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“…Several studies have discussed bivariate distributions based on copulas. These include the works of Elgohari and Yousof [38], Hamed et al [39], Aboraya et al [40], El-Sherpieny et al [41], El-Sherpieny et al [42], El-Sherpieny et al [43], Almetwally et al [44], El-Sherpieny et al [45], Muhammed et al [46], Abulebda et al [47], Hassan et al [48], Zhao et al [49], and Qura et al [50].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, assuming independence on 𝛽 1 , 𝛽 2 and 𝛽 3 , if 𝑎 = 𝑎 ̅ and 𝑏 = 𝑏 ̅ , it is easy to obtain the explicit Bayes estimators of 𝛽 1 , 𝛽 2 and 𝛽 3 using equation(48) within the SEL function. However, if 𝑎 ≠ 𝑎 ̅ and 𝑏 ≠ 𝑏 ̅ , it is impossible to obtain the Bayes estimators explicitly.…”

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confidence: 99%

Bivariate Exponentiated Lomax Distribution Based on Marshall-olkin Method With a Real-life Application

Kalantan,

EL-Helbawy,

AL-Dayian

et al. 2024

Preprint

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This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Numerous attributes are examined, including the joint reliability and hazard functions, the bivariate probability density function, and its marginal. The joint probability density function and joint cumulative distribution function can be stated analytically. Different contour plots of the joint probability density function, joint reliability, joint hazard rate functions of the bivariate exponentiated Lomax distribution are given. The unknown parameters, reliability, and hazard rate functions of the bivariate exponentiated Lomax distribution are estimated using the maximum likelihood method. Also, Bayesian technique is applied to derive the Bayes estimators, reliability and hazard rate functions of the bivariate exponentiated Lomax distribution. In addition, maximum likelihood and Bayesian two-sample prediction is considered to predict a future observation from a future sample of the bivariate exponentiated Lomax distribution. Finally, a numerical illustration is presented, including a simulation study to investigate the theoretical findings derived in this paper of the maximum likelihood and Bayesian estimation. Also, a simulation study is provided to evaluate the theoretical outcomes and performance of the maximum likelihood and Bayesian predictors. Furthermore, the real data set used in this paper is the scoring times from 42 American Football League matches that took place over three consecutive independent weekends in 1986. The results of utilizing the real data approves the practicality and flexibility of the bivariate exponentiated Lomax distribution in real-world situations and that the bivariate exponentiated Lomax distribution is suitable for modeling this bivariate data set. Mathematics Subject Classification: 62F10, 62F15, 62N05, 62E10, 62N0

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“…The authors in [14] developed and presented applications for 2D copulas using the counter-monotonic shock method. Based on the FGM copula, the authors in [15] proposed a 2D generalized half-logistic distribution and its application to household financial affordability in KSA. The author of [16] proposed a new collection of new trigonometric and hyperbolic FGM-type copulas.…”

Section: Introductionmentioning

confidence: 99%

A Collection of Two-Dimensional Copulas Based on an Original Parametric Ratio Scheme

Chesneau

2023

Symmetry

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The creation of two-dimensional copulas is crucial for the proposal of novel families of two-dimensional distributions and the analysis of original dependence structures between two quantitative variables. Such copulas can be developed in a variety of ways. In this article, we provide theoretical contributions to this subject; we emphasize a new parametric ratio scheme to create copulas of the following form: C(x,y)=(b+1)xy/[b+ϕ(x,y)], where b is a constant and ϕ(x,y) is a two-dimensional function. As a notable feature, this form can operate an original trade-off between the product copula and more versatile copulas (not symmetric, with tail dependence, etc.). Instead of a global study, we examine seven concrete examples of such copulas, which have never been considered before. Most of them are extended versions of existing non-ratio copulas, such as the Celebioglu–Cuadras, Ali-Mikhail-Haq, and Gumbel–Barnett copulas. We discuss their attractive properties, including their symmetry, dominance, dependence, and correlation features. Some graphics and tables are given as complementary works. Our findings expand the horizons of new two-dimensional distributional or dependence modeling.

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Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA

Cited by 7 publications

References 13 publications

Bivariate power Lomax distribution with medical applications

Bivariate power Lomax distribution with medical applications

Bivariate Exponentiated Lomax Distribution Based on Marshall-olkin Method With a Real-life Application

A Collection of Two-Dimensional Copulas Based on an Original Parametric Ratio Scheme

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