Inequalities involving moments of a continuous random variable defined over a finite interval (Q1767933)

The aim of this paper is to obtain alternative estimations for the moments of a continuous random variable whose probability distribution is a convex function on the interval of real numbers. Korkine's identity and integral inequalities of Hölder and Grüss are the main technical tools used to derive inequalities involving higher moments, special means and moment evaluation of beta distributions. These results have direct applications in insurance problems, where the insurer's payment on a given contract or group of contracts follows a mixture of compound probability distribution.