  Introducing the discrete probability distribution by means of the Prabhakar
(or the three--parameter Mittag--Leffler) function, we establish explicit
expressions for raw and factorial moments and also general fractional order
moments. Applying an elementary moment inequality we obtain functional upper
bounds for the Tur\'anian difference for Prabhakar function. Finally, a
Laguerre inequality is proved and functional upper bound has been given for
Laguerreian difference for Prabhakar function.
