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<p>Developing a refined approach for constructing probability distribution functions of dependent variables defined over a Cartesian layout is essential for accurately characterizing the joint behaviour of multiple variables while avoiding the computational complexity associated with traditional inversion techniques, particularly in stochastic problem. In this study, we propose a novel method for deriving the (transition) distribution function over a Cartesian framework linking the random vector <i>rv</i> <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{t}=(t_{0},t_{1},...,t_{n})^{\prime }\)</EquationSource> </InlineEquation> and multivariate <i>rv</i>’s <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textbf{X}=(X_{1},...,X_{k})\)</EquationSource> </InlineEquation>. The method was based on a copula representation of the multivariate Johnson’s Systems of Distribution (JSD), developed through JSD contingency layout transformation. Several theoretical properties of the proposed multivariate JSD copula model were established, including the time-dependent (object-dependent) correlation matrix, mutual information and key stochastic characteristics. Model parameters were estimated using maximum likelihood and numerical optimization techniques. The effectiveness of the proposed model was demonstrated through applications in time-series, behavioural, and survival analyses.</p>

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Stochastic copula modelling of multivariate Johnson’s Systems of Distribution

  • 期刊论文

  • 发表日期：

    2026年1月17日

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  • Ajibola Taiwo Sóyínká,
  • Akin Adeseye Olósundé,
  • Atinuke Olusola Adébánjí

摘要

Developing a refined approach for constructing probability distribution functions of dependent variables defined over a Cartesian layout is essential for accurately characterizing the joint behaviour of multiple variables while avoiding the computational complexity associated with traditional inversion techniques, particularly in stochastic problem. In this study, we propose a novel method for deriving the (transition) distribution function over a Cartesian framework linking the random vector rv \(\textbf{t}=(t_{0},t_{1},...,t_{n})^{\prime }\) and multivariate rv’s \(\textbf{X}=(X_{1},...,X_{k})\) . The method was based on a copula representation of the multivariate Johnson’s Systems of Distribution (JSD), developed through JSD contingency layout transformation. Several theoretical properties of the proposed multivariate JSD copula model were established, including the time-dependent (object-dependent) correlation matrix, mutual information and key stochastic characteristics. Model parameters were estimated using maximum likelihood and numerical optimization techniques. The effectiveness of the proposed model was demonstrated through applications in time-series, behavioural, and survival analyses.