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<p>We derive the exact probability density function of the product of <i>N</i> independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and characteristic function, as well as asymptotic approximations for the density, tail probabilities and quantile function. From our general results, we deduce closed-form formulas for the density, cumulative distribution function and characteristic function of the product of <i>N</i> independent asymmetric Laplace random variables and mixed products of independent Laplace and centred normal random variables.</p>

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The Variance-Gamma Product Distribution

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月23日

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  • Robert E. Gaunt,
  • Siqi Li,
  • Heather L. Sutcliffe

摘要

We derive the exact probability density function of the product of N independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and characteristic function, as well as asymptotic approximations for the density, tail probabilities and quantile function. From our general results, we deduce closed-form formulas for the density, cumulative distribution function and characteristic function of the product of N independent asymmetric Laplace random variables and mixed products of independent Laplace and centred normal random variables.