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Generalizations of distributions related to (k1,k2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_1,k_2$$\end{document})-runs

Authors
  • Kumar, A. N.1
  • Upadhye, N. S.1
  • 1 Indian Institute of Technology Madras, Department of Mathematics, Chennai, 600036, India , Chennai (India)
Type
Published Article
Journal
Metrika
Publisher
Springer Berlin Heidelberg
Publication Date
Jul 03, 2018
Volume
82
Issue
2
Pages
249–268
Identifiers
DOI: 10.1007/s00184-018-0668-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

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.

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