On runs of ones defined on a q-sequence of binary trials

Frosso S. Makri () and Zaharias M. Psillakis ()
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Frosso S. Makri: University of Patras
Zaharias M. Psillakis: University of Patras

Metrika: International Journal for Theoretical and Applied Statistics, 2016, vol. 79, issue 5, No 5, 579-602

Abstract: Abstract In a sequence of n binary ( $$0{-}1$$ 0 - 1 ) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k, $$1\le k\le n$$ 1 ≤ k ≤ n . Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.

Keywords: Binary trials; Runs; Distributions of order k; q-Distributions; Maximum likelihood estimation; Likelihood ratio test; 62Exx; 62Fxx; 65Cxx (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00184-015-0568-2

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