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Inference and application to finance of \(\Gamma\)-distributions with at most one change-point. (Chinese. English summary) Zbl 1125.62019

Summary: The change point of parameters in \(\Gamma\)-distributions is considered. Suppose that \(X_1,X_2,\dots, X_{[n\tau_0]}\), \(X_{[n\tau_0]+1}, \dots, X_n\) are independent random variables where \(X_1, X_2, \dots, X_{[n\tau_0]}\) are i.i.d. \(\sim \Gamma(x; v_1, \lambda_1)\), and \(X_{[n\tau_0]+1} , X_{[n\tau_0]+2}\), \(\dots, X_n\), are i.i.d. \(\sim \Gamma(x;v_2, \lambda_2), \tau_0\) is unknown and called change point. The distribution of the statistic proposed in the paper can be approximated by the first type of extremal distributions. Under mild conditions, the strong consistency and rate of convergence of the estimator for the change point are presented. An application is also presented.

MSC:

62F12 Asymptotic properties of parametric estimators
62P05 Applications of statistics to actuarial sciences and financial mathematics
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