ABSTRACT
Consider a random arrangement of m + n elements, m of them are one type, and n of them are of another type. A run is a sequence of symbols of the same type bounded by symbols of another type except for the first and last position. Let R denote the total number of runs in the sequence. The probability mass function of R is given by
P (R = r|m,n) = 2 ( m−1 r/2−1
) for even r, and
P (R = r|m,n) = ( m−1 (r−1)/2
) for odd r. The distribution of runs is useful to test the hypothesis of randomness of an arrangement of elements. The hypotheses of interest are
H0: arrangement is random vs. Ha: arrangement is non random.
