Abstract:
|
We study the distributions of runs and patterns in a sequence of Bernoulli trials given the number of successes (or failures). Given the number of total successes, the outcomes of a sequence of $n$ Bernoulli trials can be viewed as random permutations. This gives us distribution-free tests based on runs and patterns. Applications to statistical process control and test for randomness are given to illustrate our methods. Furthermore, we extend the results to multi-state trials.
|