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Abstract <p>We introduce a bivariate <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561168Kumar-m3--> </InlineEquation>-Weibull distribution constructed using the FGM copula, namely FGMBV<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561168Kumar-m4--> </InlineEquation>WD. The proposed FGMBV<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561168Kumar-m5--> </InlineEquation>W distribution is utilized for characterizing bivariate data, as it serves as a suitable choice for modeling non-negative real-valued data for various applications, distinct from other bivariate distributions, based on the FGM copula. We derive some general properties of the FGMBV<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561168Kumar-m6--> </InlineEquation>W distribution, including marginal and conditional distributions, and the survival function. Additionally, we explore Kendall’s <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\tau\)</EquationSource> <!--LobJMat2561168Kumar-m7--> </InlineEquation> and Spearman’s dependence measures. We employ the maximum likelihood estimation (MLE) technique to estimate the parameters of the proposed distribution. Finally, we highlight the significance of the proposed distribution on two real data sets to illustrate the applicability. A comparison is made with some baseline bivariate distributions based on the FGM copula, such as the FGM bivariate Weibull (FGMBVWD), FGM bivariate Gamma (FGMBVGD), FGM Bivariate Generalized Exponential (FGMBVGED), and bivariate <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561168Kumar-m8--> </InlineEquation>-Gaussian distribution (BV<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561168Kumar-m9--> </InlineEquation>GD).</p>

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A Copula-Based Bivariate \(\boldsymbol{q}\)-Weibull Distribution

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Pankaj Kumar,
  • Vivek Vijay

摘要

Abstract

We introduce a bivariate \(q\) -Weibull distribution constructed using the FGM copula, namely FGMBV \(q\) WD. The proposed FGMBV \(q\) W distribution is utilized for characterizing bivariate data, as it serves as a suitable choice for modeling non-negative real-valued data for various applications, distinct from other bivariate distributions, based on the FGM copula. We derive some general properties of the FGMBV \(q\) W distribution, including marginal and conditional distributions, and the survival function. Additionally, we explore Kendall’s \(\tau\) and Spearman’s dependence measures. We employ the maximum likelihood estimation (MLE) technique to estimate the parameters of the proposed distribution. Finally, we highlight the significance of the proposed distribution on two real data sets to illustrate the applicability. A comparison is made with some baseline bivariate distributions based on the FGM copula, such as the FGM bivariate Weibull (FGMBVWD), FGM bivariate Gamma (FGMBVGD), FGM Bivariate Generalized Exponential (FGMBVGED), and bivariate \(q\) -Gaussian distribution (BV \(q\) GD).