On distribution of waiting time for the first failure followed by a limited length success run

Volume 40 / 2013

Czesław Stępniak Applicationes Mathematicae 40 (2013), 421-430 MSC: Primary 62E15, 05A10; Secondary 60C05, 62N86. DOI: 10.4064/am40-4-3


Many doctors believe that a patient will survive a heart attack unless a succeeding attack occurs in a week. Treating heart attacks as failures in Bernoulli trials we reduce the lifetime after a heart attack to the waiting time for the first failure followed by a success run shorter than a given $k$. In order to test the “true” critical period of the lifetime we need its distribution. The probability mass function and cumulative distribution function of the waiting time are expressed in explicit and concise form by binomial coefficients.


  • Czesław StępniakFaculty of Mathematics and Natural Sciences
    University of Rzeszów
    Pigonia 1
    35-310 Rzeszów, Poland

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