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November, 1982 Some Limit Theorems on a Supercritical Simple Galton-Watson Process
K. N. Venkataraman, K. Nanthi
Ann. Probab. 10(4): 1075-1078 (November, 1982). DOI: 10.1214/aop/1176993731

Abstract

Let $X = (X_n; n \geq 0; X_0 = 1)$ be a supercritical Galton-Watson process possessing an offspring mean $1 < m < \infty$, and variance $0 < \sigma^2 < \infty$. The limiting distribution of $\{X^{-1/2}_n(X_{n+r} - \hat{m}^rX_n); r = 2, \cdots, T\}$ where $\hat{m} = X_{n+1}/X_n$, is obtained. As a consequence of this result a Quenouille-Bartlett type of asymptotic goodness of fit test is also proposed for the process $X$.

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K. N. Venkataraman. K. Nanthi. "Some Limit Theorems on a Supercritical Simple Galton-Watson Process." Ann. Probab. 10 (4) 1075 - 1078, November, 1982. https://doi.org/10.1214/aop/1176993731

Information

Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0498.62072
MathSciNet: MR672310
Digital Object Identifier: 10.1214/aop/1176993731

Subjects:
Primary: 62M99
Secondary: 60F99

Keywords: asymptotic goodness of fit test , Supercritical Galton-Watson process

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 4 • November, 1982
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