Log-convexity and log-concavity of noncentral gamma sums and differences

Robert E. Gaunt; Frédéric Ouimet

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arXiv · 2607.09499

Log-convexity and log-concavity of noncentral gamma sums and differences

Robert E. Gaunt·Frédéric Ouimet

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Abstract

We study log-convexity and log-concavity of densities obtained from sums and differences of two independent noncentral gamma random variables. We give a complete classification of one-sided log-convexity for noncentral gamma differences, a complete log-convexity classification for sums of two independent central gamma random variables, and sharp log-concavity criteria for central differences and for common-scale sums. As special cases, we deduce a log-convexity classification for the density of the product of two correlated normal random variables with arbitrary means and variances, and log-convexity and log-concavity classifications for the densities of the variance-gamma and McKay Type I distributions.

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BibTeX RIS

Robert E. Gaunt, Frédéric Ouimet. 2026-07-10. Log-convexity and log-concavity of noncentral gamma sums and differences. https://arxiv.org/abs/2607.09499

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