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A direct method to obtain the joint distribution of successes, failures and patterns in enumeration problems

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  • Antzoulakos, Demetrios L.
  • Boutsikas, Michael V.

Abstract

Let be a pattern (single or composite) defined over a sequence of Bernoulli trials. Let Xn, Sn and Fn be the number of occurrences of , the number of successes and the number of failures in n trials, respectively. Also let Tr, STr and FTr be the waiting time for the rth occurrence of in an infinite sequence of trials, the number of successes and the number of failures observed at that time, respectively. In this article we present some simple results revealing that, if we know either the distribution of Xn or the distribution of Tr we can instantly derive the joint distribution of (Xn,Sn,Fn) and (Tr,STr,FTr).

Suggested Citation

  • Antzoulakos, Demetrios L. & Boutsikas, Michael V., 2007. "A direct method to obtain the joint distribution of successes, failures and patterns in enumeration problems," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 32-39, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:1:p:32-39
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    References listed on IDEAS

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    1. M. Koutras, 1996. "On a waiting time distribution in a sequence of Bernoulli trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 789-806, December.
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    6. Kiyoshi Inoue, 2004. "Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 143-168, March.
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    8. Demetrios Antzoulakos & Stathis Chadjiconstantinidis, 2001. "Distributions of Numbers of Success Runs of Fixed Length in Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 599-619, September.
    9. Stathis Chadjiconstantinidis & Markos Koutras, 2001. "Distributions of the Numbers of Failures and Successes in a Waiting Time Problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 576-598, September.
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    Cited by:

    1. Frosso S. Makri & Zaharias M. Psillakis, 2011. "On Success Runs of Length Exceeded a Threshold," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 269-305, June.

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