On the BLUE of the scale parameter of the generalized Pareto distribution
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Abstract
In this article, we will study the linear estimation of the scale parameter of the generalized Pareto distribution (GPD) which has the probability density function (p.d.f.)
$$ f(x)=\left\{\begin{array}{ll} \sigma^{-1}(1-rx/\sigma)^{1/r-1},~~& r\not=0 \\ \sigma^{-1}\exp(-x/\sigma),&r=0. \end{array}\right.$$
We first derive the expected value, variances and covariances of the order statistics from the GPD. Then proceed to find the best linear unbiased estimates of the scale parameter $\sigma$ based on a few order statistics selected from a complete sample or a type-II censored sample. Results of some chosen cases were tabulated.
$$ f(x)=\left\{\begin{array}{ll} \sigma^{-1}(1-rx/\sigma)^{1/r-1},~~& r\not=0 \\ \sigma^{-1}\exp(-x/\sigma),&r=0. \end{array}\right.$$
We first derive the expected value, variances and covariances of the order statistics from the GPD. Then proceed to find the best linear unbiased estimates of the scale parameter $\sigma$ based on a few order statistics selected from a complete sample or a type-II censored sample. Results of some chosen cases were tabulated.
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Cheng, S. W., & Chou, C. H. (2000). On the BLUE of the scale parameter of the generalized Pareto distribution. Tamkang Journal of Mathematics, 31(3), 165–174. https://doi.org/10.5556/j.tkjm.31.2000.391
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