On the BLUE of the scale parameter of the generalized Pareto distribution

Authors

  • S. W. Cheng
  • C. H. Chou

DOI:

https://doi.org/10.5556/j.tkjm.31.2000.391

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.

Author Biographies

S. W. Cheng

Department of Statistics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada.

C. H. Chou

Cathay Assurance Company, Taipei, Taiwan, R.O.C.

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Published

2000-09-30

How to Cite

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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Section

Papers