A bivariate inverse Weibull distribution and its application in complementary risks model

Mondal, Shuvashree; Kundu, Debasis

doi:10.1080/02664763.2019.1669542

Cited by 15 publications

(6 citation statements)

References 16 publications

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“…The research on copula is currently ongoing, and what follows is only a short overview of recent works. On the basis of copulas, the authors in [5] suggested a 2D inverse Weibull distribution and its use in a special risk model. The authors in [6] described a method for a 2D hydrologic correlation analysis using a Bayesian model-averaging copula.…”

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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Section: Introductionmentioning

confidence: 99%

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

Chesneau

2023

Symmetry

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“…Muhammed [15] proposed a bivariate generalized Kumaras-wamy distribution. A bivariate inverse Weibull distribution has been developed by Mondal and Kundu [16]. Darwish and Shahbaz [17] formulated a bivariate transmuted Burr distribution; see also [18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

A New Bivariate Extended Generalized Inverted Kumaraswamy Weibull Distribution

Ragab

Elhassanein

2022

Advances in Mathematical Physics

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This article presents a new bivariate extended generalized inverted Kumaraswamy Weibull (BIEGIKw-Weibull) distribution with nine parameters. Statistical properties of the new distribution are discussed. Forms of copulas, moments, conditional moments, bivariate reliability function, and bivariate hazard rate function are derived. Maximum likelihood estimators are formulated. Simulation is conducted for three different sets of parameters to verify the theoretical results and to discuss the new distribution properties. The performance of the maximum likelihood method is investigated via Monte Carlo simulation depending on the bias and the standard error. Simulated lifetime data is used as an application of the new model.

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“…Employing the conversion algorithm of Gamma distribution to Gaussian distribution, a newly invented actual precipitation index (API) is applied to classify the characteristics of droughts to explain the precipitation data S ¸en and Almazroui (2021). There are various well-known algorithms to extend Uni-variate to Bi-variate distribution like the Marshall-Olkin technique Mondal and Kundu (2020), copula approach El-Sherpieny et al ( 2021), application of the probability distribution of a concomitant of an order statistic Thomas and Jose (2020), and so on.…”

Section: Introductionmentioning

confidence: 99%

Uni-variate and Bi-variate Inverted Exponential-Teissier Distribution in Bayesian and Non-Bayesian framework to Model Stochastic Dynamic Variation of Climate data

THAKUR

Bhattacharya

Das

2022

Preprint

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This article provides a new Inverted Exponential Teissier (IET) distribution to model an extreme value data set and explain temporal dependence in environmental statistics employing Bi-variate probability distribution. We deduce its various statistical properties, including descriptive statistics, characterization, and different measurements of reliability. The model parameters are estimated using Bayesian and Non-Bayesian frameworks. For exploring the dependency structures between two geographical Random Variables (RV), we extend the IET to Bivariate IET distribution, (BIET). We introduce a novel time-series forecasting algorithm based upon copula assuming stationarity of the data set. We validate the proposed method using extensive simulation studies with different possible combinations of parameter values. This method is applied to the seasonal rainfall data of Kerala from 1901 to 2017. We estimate the monsoon rainfall using median regression derived from BIET, where summer rainfall data is used as an important covariate. We found the Mean Absolute Percentage Error (MAPE) is 19.242% on the test data set.

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A bivariate inverse Weibull distribution and its application in complementary risks model

Cited by 15 publications

References 16 publications

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

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

A New Bivariate Extended Generalized Inverted Kumaraswamy Weibull Distribution

Uni-variate and Bi-variate Inverted Exponential-Teissier Distribution in Bayesian and Non-Bayesian framework to Model Stochastic Dynamic Variation of Climate data

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