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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 3, Pages 623–633
(Mi tvp3308)
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This article is cited in 5 scientific papers (total in 5 papers)
Short Communications
On the statistics of branching processes
N. M. Yanev Sofia, Bulgaria
Abstract:
Let $\mu_t(n)$, $t=0,1,2,\dots,$ 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.
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
Linking options:
https://www.mathnet.ru/eng/tvp3308 https://www.mathnet.ru/eng/tvp/v20/i3/p623
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Abstract page: | 221 | Full-text PDF : | 117 |
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