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A quantile estimation for massive data with generalized Pareto distribution

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  • Song, Jongwoo
  • Song, Seongjoo

Abstract

This paper proposes a new method of estimating extreme quantiles of heavy-tailed distributions for massive data. The method utilizes the Peak Over Threshold (POT) method with generalized Pareto distribution (GPD) that is commonly used to estimate extreme quantiles and the parameter estimation of GPD using the empirical distribution function (EDF) and nonlinear least squares (NLS). We first estimate the parameters of GPD using EDF and NLS and then, estimate multiple high quantiles for massive data based on observations over a certain threshold value using the conventional POT. The simulation results demonstrate that our parameter estimation method has a smaller Mean square error (MSE) than other common methods when the shape parameter of GPD is at least 0. The estimated quantiles also show the best performance in terms of root MSE (RMSE) and absolute relative bias (ARB) for heavy-tailed distributions.

Suggested Citation

  • Song, Jongwoo & Song, Seongjoo, 2012. "A quantile estimation for massive data with generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 143-150, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:143-150
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    Citations

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    Cited by:

    1. Castillo, Joan del & Serra, Isabel, 2015. "Likelihood inference for generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 116-128.
    2. Federico Palacios-González & Rosa M. García-Fernández, 2020. "A faster algorithm to estimate multiresolution densities," Computational Statistics, Springer, vol. 35(3), pages 1207-1230, September.
    3. Park, Myung Hyun & Kim, Joseph H.T., 2016. "Estimating extreme tail risk measures with generalized Pareto distribution," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 91-104.
    4. Xu Zhao & Zhongxian Zhang & Weihu Cheng & Pengyue Zhang, 2019. "A New Parameter Estimator for the Generalized Pareto Distribution under the Peaks over Threshold Framework," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    5. Hideki Nagatsuka & N. Balakrishnan, 2021. "Efficient likelihood-based inference for the generalized Pareto distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1153-1185, December.

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