Waiting for Scans Containing Two Successes

Markos V. Koutras () and Spiros D. Dafnis ()
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Markos V. Koutras: University of Piraeus, Department of Statistics and Insurance Science, School of Finance and Statistics
Spiros D. Dafnis: University of Piraeus, Department of Statistics and Insurance Science, School of Finance and Statistics

Chapter 39 in Handbook of Scan Statistics, 2024, pp 757-793 from Springer

Abstract: Abstract In the present chapter, we present a review of results pertaining to the distribution of waiting times for the occurrence(s) of scans of type 2∕r in sequences of binary trials. Our review covers the geometric distribution of order 2∕r, the negative binomial distributions of order 2∕r, and their generalizations. Exact and asymptotic results are presented and illustrated through numerical examples. In the case of the geometric distribution of order 2∕r, a new closed, exact formula is established. Several applications of the reviewed waiting time distributions in various scientific areas are discussed in some detail.

Keywords: Binary trials; Scan waiting time distributions; Distributions of order 2∕r; Markov chain approach; Multiple scan occurrences (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-1-4614-8033-4_57

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