Modified maximum spacings method for generalized extreme value distribution and applications in real data analysis. (English) Zbl 1305.62201
Summary: This paper analyzes weekly closing price data of the S&P 500 stock index and electrical insulation element lifetimes data based on generalized extreme value distribution. A new estimation method, modified maximum spacings (MSP) method, is proposed and obtained by using interior penalty function algorithm. The standard error of the proposed method is calculated through Bootstrap method. The asymptotic properties of the modified MSP estimators are discussed. Some simulations are performed, which show that the proposed method is not only available for the whole shape parameter space, but is also of high efficiency. The benchmark risk index, value at risk (VaR), is evaluated according to the proposed method, and the confidence interval of VaR is also calculated through Bootstrap method. Finally, the results are compared with those derived by empirical calculation and some existing methods.
MSC:
| 62G32 | Statistics of extreme values; tail inference |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 91G70 | Statistical methods; risk measures |
Keywords:
Box-Cox transformation; generalized extreme value distribution; maximum spacings estimate; interior penalty function algorithm; bootstrap method; value at riskReferences:
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