Formulae and recursions for the joint distribution of success runs of several lengths
Document Type
Article
Publication Date
1-1-1997
Abstract
Consider a sequence of n independent Bernoulli trials with the j-th trial having probability Pj of success, 1 ≤ j ≤ n. Let M(n, K) and N(n,K) denote, respectively, the r-dimensional random variables (M(n, k1), ..., M(n,kr)) and (N (n, k1),..., N(n, kr)), where K = (k1, k2,..., kr) and M(n, s) [N(n, s)] represents the number of overlapping [non-overlapping] success runs of length s. We obtain exact formulae and recursions for the probability distributions of M(n, K) and N(n, K). The techniques of proof employed include the inclusion-exclusion principle and generating function methodology. Our results have potential applications to statistical tests for randomness.
Publication Title
Annals of the Institute of Statistical Mathematics
Recommended Citation
Godbole, A.,
Papastavridis, S.,
&
Weishaar, R.
(1997).
Formulae and recursions for the joint distribution of success runs of several lengths.
Annals of the Institute of Statistical Mathematics,
49(1), 141-153.
http://doi.org/10.1023/A:1003170823986
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/8209