The exact and asymptotic distribution of overlapping success runs
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 21 (4) , 953-967
- https://doi.org/10.1080/03610929208830825
Abstract
Let M = Mn,k and N = Nn,k denote, respectively, the number of overlapping and non-overlapping success runs of fixed length k in n Bernoulli (p) trials. We derive an alternative formula for P(M = x) which is substantially simpler to apply than the one in Ling (1988). Our method of proof brings out several connections between the distributions of M and N. Poisson approximations and a Berry-Esséen theorem are obtained for M, and applications are indicated.Keywords
This publication has 13 references indexed in Scilit:
- Poisson approximations for runs and patterns of rare eventsAdvances in Applied Probability, 1991
- m-consecutive-k-out-of-n:F systemsIEEE Transactions on Reliability, 1990
- Specific formulae for some success run distributionsStatistics & Probability Letters, 1990
- A new class of negative binomial distributions of orderStatistics & Probability Letters, 1989
- Two Moments Suffice for Poisson Approximations: The Chen-Stein MethodThe Annals of Probability, 1989
- On binomial distributions of order kStatistics & Probability Letters, 1988
- Successes, runs and longest runsStatistics & Probability Letters, 1986
- Multiple comparisons and sums of dissociated random variablesAdvances in Applied Probability, 1985
- The asymptotic distributions of incomplete U-statisticsProbability Theory and Related Fields, 1984
- The Distribution Theory of RunsThe Annals of Mathematical Statistics, 1940