THE DENSITY FUNCTION OF THE FIRST OCCURRENCE OF A BINARY PATTERN

The probability density function associated with the first occurrence of a binary pattern in a sequence of independent Bernoulli trials was given in McDermott and Sheahan. We give a simpler expression for it in terms of a unique family of homogeneous polynomials in two variables. In the process, we...

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Bibliographic Details
Published in:Mathematical proceedings of the Royal Irish Academy 2009-10, Vol.109A (2), p.123-136
Main Author: Barry, Michael J.J.
Format: Article
Language:English
Subjects:
Coefficients
Generating function
Integers
Mathematical sequences
Polynomials
Recurrence relations
Online Access:Get full text
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Summary:The probability density function associated with the first occurrence of a binary pattern in a sequence of independent Bernoulli trials was given in McDermott and Sheahan. We give a simpler expression for it in terms of a unique family of homogeneous polynomials in two variables. In the process, we obtain a recurrence relation for the density function and we study the coefficients of the homogeneous polynomials.
ISSN:1393-7197
2009-0021
2009-0021
DOI:10.1353/mpr.2009.0000