Recently, the concept of rank selection probabilities for stack filter
s have been introduced. If the probablities are known, then the output
distribution for i.i.d. input follows easily. There is another expres
sion for the output distribution of a stack filter using certain quant
ities called A(i). In this correspondence, we utilize the different fo
rms of output distribution to derive a simple connection between the q
uantities A(i) and the rank selection probabilities. This also leads t
o a new fast method for the computation of rank selection probabilitie
s.