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Probabilistic properties of second order branching process

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  • Akanksha Kashikar
  • S. Deshmukh

Abstract

The classical BGW process assumes first order dependence, whereas many real life datasets exhibit a second or higher order dependence. Further, in some situations, there is a need for a model which allows for simultaneous reproduction by a parent and its offspring. This paper proposes a second order branching process model to accommodate such situations and discusses its probabilistic properties such as extinction probability and limiting behaviour of the generation sizes. Estimation of offspring means and growth rate are also discussed. This model is further used to model the swine flu data for Pune, India, and La-Gloria, Mexico. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Akanksha Kashikar & S. Deshmukh, 2015. "Probabilistic properties of second order branching process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 557-572, June.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:3:p:557-572
    DOI: 10.1007/s10463-014-0462-0
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    References listed on IDEAS

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    1. Ross Sparks & Tim Keighley & David Muscatello, 2010. "Early warning CUSUM plans for surveillance of negative binomial daily disease counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(11), pages 1911-1929.
    2. Kashikar, Akanksha S. & Deshmukh, S.R., 2012. "Second order branching process with continuous state space," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1930-1934.
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