On the ABLUE of the scale parameter of the generalized Pareto distribution
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Abstract
We study the asymptotic best linear unbiased estimation of the scale parameter of the generalized Pareto distribution (GPD) with the probability density function (p.d.f.)
$$ f(x)=\left\{\begin{array}{ll} \sigma^{-1}(1-rx/\sigma)^{1/r-1},~~&r\not=0 \\ \sigma^{-1}\exp(-x/\sigma),~~&r=0. \end{array}\right.$$
In Cheng and Chou (2000), the best linear unbiased estimation of the scale parameter was discussed for finite samples. We study the large sample size cases here. Results of some chosen cases are tabulated.
$$ f(x)=\left\{\begin{array}{ll} \sigma^{-1}(1-rx/\sigma)^{1/r-1},~~&r\not=0 \\ \sigma^{-1}\exp(-x/\sigma),~~&r=0. \end{array}\right.$$
In Cheng and Chou (2000), the best linear unbiased estimation of the scale parameter was discussed for finite samples. We study the large sample size cases here. Results of some chosen cases are tabulated.
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Cheng, S. W., & Chou, C. H. (2000). On the ABLUE of the scale parameter of the generalized Pareto distribution. Tamkang Journal of Mathematics, 31(4), 317–330. https://doi.org/10.5556/j.tkjm.31.2000.390
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