On the multivariate distributions of order statistics of discrete-state processes

The authors consider the problem of determining the multivariable joint probability distributions of the order statistics of discrete-state processes whose elements are independent and identically distributed. Two methods, the indirect and direct methods, are presented and compared in terms of their inherent computational complexity. Recursive formulae are derived which give the number of floating point multiplications required. Utilizing these formulae, it was found that, in order to calculate the m-variate distribution of a discrete-state process with L elements, the indirect method was more efficient than the direct method for L>10 (m-1)