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Teor. Veroyatnost. i Primenen., 1975, Volume 20, Issue 3, Pages 623–633 (Mi tvp3308)  

Short Communications

On the statistics of branching processes

N. M. Yanev

Sofia, Bulgaria

Abstract: Let $\mu_t(n)$, $t=0,1,2,…,$ be a Galton–Watson process, starting from $n$ particles. We show that when $n,t\to\infty$ the estimator
$$ \widehat A_t(n)=\frac{\sum_{k=1}^t\mu_k(n)}{\sum_{k=0}^{t-1}\mu_k(n)} $$
for the expectation $A=\mathbf E\mu_1(1)$ is consistent and asymptoticaly unbiased. We obtain limit distributions for $\widehat A_t(n)$ in the subcritical, critical and supercritical cases.

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English version:
Theory of Probability and its Applications, 1976, 20:3, 612–622

Bibliographic databases:

Received: 17.03.1975

Citation: N. M. Yanev, “On the statistics of branching processes”, Teor. Veroyatnost. i Primenen., 20:3 (1975), 623–633; Theory Probab. Appl., 20:3 (1976), 612–622

Citation in format AMSBIB
\Bibitem{Yan75}
\by N.~M.~Yanev
\paper On the statistics of branching processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 3
\pages 623--633
\mathnet{http://mi.mathnet.ru/tvp3308}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=381191}
\zmath{https://zbmath.org/?q=an:0363.60073}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 20
\issue 3
\pages 612--622
\crossref{https://doi.org/10.1137/1120066}


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