<p>This article explores the properties and application of a modified Greenwood statistic for multivariate random samples, specifically those derived from multivariate Pareto and multivariate Student’s t distributions. Both distribution families are characterized by heavy tails and dependence structure provided by mixing. We investigate the stochastic order of the modified Greenwood statistic discussed for these multivariate samples, demonstrating its utility in goodness-of-fit testing. Furthermore, the modified Greenwood statistic is proposed for the broader problem of identifying whether a random sample originates from a distribution with infinite variance. The proposed testing methodology is validated through Monte Carlo simulations and applied to multidimensional data in real-world technical diagnostics (vibration signals) and financial analysis, showcasing its effectiveness in practical scenarios.</p>