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In this paper we introduce a novel statistical framework based on the firsttwo quantile conditional moments that facilitates effective goodness-of-fittesting for one-sided L\'evy distributions. The scale-ratio frameworkintroduced in this paper extends our previous results in which we have shownhow to extract unique distribution features using conditional variance ratiofor the generic class of {\alpha}-stable distributions. We show that theconditional moment-based goodness-of-fit statistics are a good alternative toother methods introduced in the literature tailored to the one-sided L\'evydistributions. The usefulness of our approach is verified using an empiricaltest power study. For completeness, we also derive the asymptotic distributionsof the test statistics and show how to apply our framework to real data.

Goodness-of-fit tests for the one-sided L\'evy distribution based on quantile conditional moments