The probability distribution and the expected value of a stopping variable associated with one-sided cusum procedures for non-negative integer valued random variables |
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Authors: | S. Zacks |
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Affiliation: | Department of Mathematical Sciences , SUNY , Binghamton |
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Abstract: | The structure of a stopping variable N based on one-sided CUSUM procedures is analyzed. Stopping occurs when a Markovian sequence of maxima of partial sums {M } crosses a certain boundary. On the basis of a recursive relationship between the Mn+1 and Mn a recursive equation is derived for the determination of the defective distributions Kn(x) = P{M ≤ x, N ≤n} . This recursive equation yields a recursive algorithm for the determination of P {N > n} . The paper studies the case when the basic random variables are non-negative integers-valued. In these cases the values of P{N > n} and E{N} can be determined by solving proper systems of linear equations. |
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Keywords: | one-sided CUSUM stopping vaariable average run length pnobability of false-alarm change-point) detection |
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