Probability Generating Functions for Discrete Real-Valued Random Variables

M. L. Esquível
2008 Theory of Probability and its Applications  
The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random variables this technique. Being so, the purpose of this work is twofold. Firstly we show that discrete
more » ... show that discrete random variables taking real values, non necessarily integer or rational, may be studied with probability generating functions. Secondly we intend to draw attention to some practical ways of performing the necessary calculations.
doi:10.1137/s0040585x97982852 fatcat:dea2qrbkvzcqvops3yre526b2y