Abstract

In this paper we consider a formula to get the exact number of nonnegative integer solution of the equality a1x1 + a2x2 + . . . + arxr = n where a1, a2, . . . , ar and n are fixed integers. Using the obtained formula, we provide a program to list the solutions for every n and a1, . . . , ar by Pascal compiler. We then obtain the distribution of an arbitrary linear combination of discrete random variables based on the proposed algorithm. We also apply the algorithm to obtain the Maximum Likelihood estimation of the parameters of the distribution. The accuracy of the algorithm was illustrated using various examples.