Maximum likelihood estimators in a statistical model of natural catastrophe claims with trend. (English) Zbl 1087.62118
The catastrophe claims form a sequence \(\{X_1,\dots,X_n\}\) of independent r.v.s with CDFs \(F_i\). In the Nevzorov record model \( F_i=F^{\gamma^{i-1}}\) only record indicators \(I_i=\mathbf{1}\{X_i>\max\{X_1,\dots,X_{i-1}\}\}\) are observed. In the three-parameter model \(F_i(x)=\exp(-\gamma^{i-1}(Ax)^{-\alpha})\), \(x>0\) and \(X_i\) are observed. The maximum likelihood estimators for the “trend” parameter \(\gamma\) are constructed in both models and their asymptotic normality is demonstrated. Analysis of data on hurricane (US) and taifun (Japan) events claims is considered.
Reviewer: R. E. Maiboroda (Kyïv)
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62G32 | Statistics of extreme values; tail inference |
| 62F12 | Asymptotic properties of parametric estimators |
Software:
ismevReferences:
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