Run statistics in a sequence of arbitrarily dependent binary trials |
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| Authors: | Sevcan Demir Serkan Eryılmaz |
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| Affiliation: | (1) Center for Computational Geostatistics (CCG), University of Alberta, Edmonton, AB, Canada;(2) Department of Civil and Environmental Engineering, 5-052 Markin/CNRL Natural Resources Engineering Facility, T6G 2W2 Edmonton, AB, Canada;(3) Quantitative Stratigraphy, Earth Sciences Research and Development, Chevron Energy Technology Company, Houston, TX, USA |
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| Abstract: | Let {Z i } i≥1 be an arbitrary sequence of trials with two possible outcomes either success (1) or failure (0). General expressions for the exact distributions of runs, both success and failure, in Z 1, . . . , Z n are presented. Our method is based on the use of joint distribution of success and failure run lengths and unifies the results on distribution of runs. As a special case of our results we obtain the distributions of runs for various binary sequences. As illustrated in the paper the results enable us to derive the distribution of runs for binary trials arising in urn models. |
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