{"ID":6497642,"CreatedAt":"2026-07-13T01:19:40.13847098Z","UpdatedAt":"2026-07-14T01:36:59.12045529Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.09499","arxiv_id":"2607.09499","title":"Log-convexity and log-concavity of noncentral gamma sums and differences","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.","short_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...","url_abs":"https://arxiv.org/abs/2607.09499","url_pdf":"https://arxiv.org/pdf/2607.09499v1","authors":"[\"Robert E. Gaunt\",\"Frédéric Ouimet\"]","published":"2026-07-10T15:15:36Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.CA\",\"math.ST\"]","methods":"[]","has_code":false}