The density function of the first occurrence of a binary pattern
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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.
RightsThis article was selected and published in Royal Irish Academy ©2009 Barry. All rights reserved.
CitationBarry. M.J.J. (2009). The density function of the first occurrence of a binary pattern. Royal Irish Academy, 109A(2): 123-136. Retrieved from http://www.jstor.org/stable/40656996
Original manuscript prior to peer review (preprint)