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Record Values of a Family of Branching Processes

  • Ibrahim Rahimov
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)

Abstract

Let
$$ {{\text{X}}_{\text{1}}}\left( {\text{t}} \right){\text{, }}{{\text{X}}_{\text{2}}}\left( {\text{t}} \right), \ldots .,{\text{t}} \in {{\text{N}}_0} = \{ 0,{\text{1,}} \ldots \} $$
, be a sequence of discrete time branching processes. We introduce the following assumptions:
$$ {X_i}\left( t \right),i \geqslant 1 $$
(a)
, are independent for any fixed
$$ t \in {N_0}{\text{ and }}{X_i}\left( 0 \right) = 1,i \geqslant 1; $$
$$ P\left\{ {{X_i}\left( t \right) = k\left| {{X_i}\left( 0 \right) = 1} \right.} \right\} = {P_k},k = 0,1, \ldots ,\sum\nolimits_{k = 0}^\infty {{P_k} = 1} $$
(b)
.

Keywords

Limit Theorem Gamma Distribution Explicit Formula Middle East Critical Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Ahsanullah M., Introduction to Record Statistics, Ginn Press, Needham Heights, MA (1988).Google Scholar
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    Athrea K.B., Ney, P.E. Branching process, Springer Verlag (1972).CrossRefGoogle Scholar
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    Nagaraja H.N. Record Values and Related Statistics - a review, Commum. Statist. Theory. Math., 17, pp. 2223–2238 (1988).MathSciNetCrossRefGoogle Scholar
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    Nevzorov V.B. Records, The Theory of Probability and its Application,32, pp. 219–251 (1987).MathSciNetzbMATHGoogle Scholar
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    Slack, R.S. A Branching Process with mean one and possibly infinite variance, Z. Wahzsch. Vezb. Geb. 9(2), pp. 139–145 (1968).MathSciNetCrossRefGoogle Scholar
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    Sevastyanov B.A., Branching Process, Nauka, Moscow (1971).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ibrahim Rahimov
    • 1
    • 2
  1. 1.Department of Statistics of Middle East Technical UniversityAnkaraTurkey
  2. 2.Mathematical Institute of AS of UzbekistanTashkentTurkey

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