pp 1–20 | Cite as

Generalizations of distributions related to (\(k_1,k_2\))-runs

  • A. N. Kumar
  • N. S. Upadhye


The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these setups and their waiting time. Also, explicit forms of probability generating function and probability mass function are obtained. Finally, two applications to demonstrate the relevance of the results are given.


(\(k_1, k_2\))-runs Waiting time Probability generating function Probability mass function Moments Markov dependent trials 

Mathematics Subject Classification

Primary 60E05 62E15 Secondary 60C05 60E10 



The authors are grateful to the associate editor and reviewers for many valuable suggestions, critical comments which improved the presentation of the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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