Success Run Waiting Times and Fuss-Catalan Numbers
Joint Authors
Source
Journal of Probability and Statistics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-09-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of k consecutive successes in a sequence of independent Bernoulli trials, that is, the geometric distribution of order k .
We show that the series coefficients are Fuss-Catalan numbers and write the roots in terms of the generating function of the Fuss-Catalan numbers.
Our main result is a new exact expression for the distribution, which is more concise than previously published formulas.
Our work extends the analysis by Feller, who gave asymptotic results.
We obtain quantitative improvements of the error estimates obtained by Feller.
American Psychological Association (APA)
Dilworth, S. J.& Mane, S. R.. 2015. Success Run Waiting Times and Fuss-Catalan Numbers. Journal of Probability and Statistics،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1069997
Modern Language Association (MLA)
Dilworth, S. J.& Mane, S. R.. Success Run Waiting Times and Fuss-Catalan Numbers. Journal of Probability and Statistics No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1069997
American Medical Association (AMA)
Dilworth, S. J.& Mane, S. R.. Success Run Waiting Times and Fuss-Catalan Numbers. Journal of Probability and Statistics. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1069997
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1069997