{"ID":2823976,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24128","arxiv_id":"2512.24128","title":"A goodness-of-fit test for the Zeta distribution with unknown parameter","abstract":"We introduce a new goodness-of-fit test for count data on $\\mathbb{N}$ for the Zeta distribution with unknown parameter. The test is built on a Stein-type characterization that uses, as Stein operator, the infinitesimal generator of a birth-death process whose stationary distribution is Zeta. The resulting $L^2$-type statistic is shown to be omnibus consistent, and we establish the limit null behavior as well as the validity of the associated parametric bootstrap procedure. In a Monte Carlo simulation study, we compare the proposed test with the only existing Zeta-specific procedure of Meintanis (2009), as well as with more general competitors based on empirical distribution functions, kernel Stein discrepancies and other Stein-type characterizations.","short_abstract":"We introduce a new goodness-of-fit test for count data on $\\mathbb{N}$ for the Zeta distribution with unknown parameter. The test is built on a Stein-type characterization that uses, as Stein operator, the infinitesimal generator of a birth-death process whose stationary distribution is Zeta. The resulting $L^2$-type s...","url_abs":"https://arxiv.org/abs/2512.24128","url_pdf":"https://arxiv.org/pdf/2512.24128v1","authors":"[\"Bruno Ebner\",\"Daniel Hlubinka\"]","published":"2025-12-30T10:22:09Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}