Thanit NanthanasubBoriboon NovaprateepNarongpol WichailukkanaMahidol UniversityFaculty of Medicine, Siriraj Hospital, Mahidol UniversityBangkok Produce Merchandising Public Company Limited2020-01-272020-01-272019-12-01Advances in Difference Equations. Vol.2019, No.1 (2019)16871847168718392-s2.0-85071954056https://repository.li.mahidol.ac.th/handle/20.500.14594/51198© 2019, The Author(s). This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties. One of our results contradicts the conjecture proposed by Neumann in 2007 which states that modified Bessel function of the first kind Iν is log-concave in (0 , ∞) given ν> 0. The log-concavity holds true in some bounded domain. The application of the other results in Kibble’s bivariate gamma distribution is also demonstrated.Mahidol UniversityMathematicsArticleSCOPUS10.1186/s13662-019-2309-8