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  • 1
    Electronic Resource
    Electronic Resource
    Joint Distributions of Numbers of Success-Runs and Failures Until the First Consecutive k Successes in a Binary Sequence (1997)
    Springer
    Annals of the Institute of Statistical Mathematics 49 (1997), S. 519-529 
    Details
    ISSN: 1572-9052
    Keywords: Probability generating function ; waiting time ; binary sequence of order k ; geometric distribution of order k
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Joint distributions of the numbers of failures, successes andsuccess-runs of length less than k until the first consecutive k successesin a binary sequence were derived recently by Aki and Hirano (1995, Ann.Inst. Statist. Math., 47, 225-235). In this paper, we present an alternatederivation of these results and also use this approach to establish someadditional results. Extensions of these results to binary sequences of orderh are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003170829230
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  • 2
    Electronic Resource
    Electronic Resource
    Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures (2000)
    Springer
    Annals of the Institute of Statistical Mathematics 52 (2000), S. 184-196 
    Details
    ISSN: 1572-9052
    Keywords: Probability generating function ; runs ; start-up demonstration test
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The probability generating function of number of trials for the start-up demonstration test with rejection upon d failures is derived. The exact distribution of the number of trials is obtained. Some recurrence relations for the probabilities are also established. The average length of the test is derived. Some illustrative examples are finally presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004101402897
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  • 3
    Electronic Resource
    Electronic Resource
    Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials (1996)
    Springer
    Annals of the Institute of Statistical Mathematics 48 (1996), S. 773-787 
    Details
    ISSN: 1572-9052
    Keywords: Probability generating function ; diserete distributions ; sooner and later problem ; success and failure runs ; Markov chain ; waiting time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The probability generating functions of the waiting times for the first success run of length k and for the sooner run and the later run between a success run of length k and a failure run of length r in the second order Markov dependent trials are derived using the probability generating function method and the combinatorial method. Further, the systems of equations of 2.m conditional probability generating functions of the waiting times in the m-th order Markov dependent trials are given. Since the systems of equations are linear with respect to the conditional probability generating functions, they can be solved exactly, and hence the probability generating functions of the waiting time distributions are obtained. If m is large, some computer algebra systems are available to solve the linear systems of equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00052332
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  • 4
    Electronic Resource
    Electronic Resource
    Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions (1997)
    Springer
    Annals of the Institute of Statistical Mathematics 49 (1997), S. 155-169 
    Details
    ISSN: 1572-9052
    Keywords: Probability generating function ; discrete distributions ; run ; start-up demonstration test ; Markov chain ; waiting time
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A general probability model for a start-up demonstration test is studied. The joint probability generating function of some random variables appearing in the Markov dependence model of the start-up demonstration test with corrective actions is derived by the method of probability generating function. By using the probability generating function, several characteristics relating to the distribution are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003122908057
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