A robust and efficient estimator for the tail index of inverse Pareto distribution

Research output: Contribution to journalArticle

Abstract

Based on the probability integral transform statistic, Finkelstein et al. (2006) have proposed a robust estimator for the shape parameter of Pareto distribution. In this paper, based on the same method, a robust and efficient estimator for the shape parameter of the inverse Pareto distribution is developed assuming that the threshold parameter is known. To study the robustness properties of this new estimator, we derive the asymptotic variance, breakdown point and gross error sensitivity. However, since the inverse Pareto distribution is literally an inverse of the Pareto distribution, some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by Finkelstein et al. (2006). The performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study. For the application, an inverse Pareto distribution is fitted to the lower tail data of Malaysian household incomes for the year of 2014, involving the proposed estimator in order to allow for the presence of outliers. Based on the inverse Pareto model, the parametric Lorenz curve is fitted and the Gini coefficient is estimated to measure the income inequality of poor households in Malaysia.

Original languageEnglish
Pages (from-to)431-439
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Volume517
DOIs
Publication statusPublished - 1 Mar 2019

Fingerprint

Tail Index
Pareto Distribution
Efficient Estimator
Robust Estimators
estimators
Estimator
Shape Parameter
Integral Transform
income
Statistic
integral transformations
Gross Error Sensitivity
Gini Coefficient
Lorenz Curve
Parametric Curves
Breakdown Point
Threshold Parameter
Malaysia
Asymptotic Variance
statistics

Keywords

  • Inverse Pareto distribution
  • Inverse Pareto tail index
  • M-estimator
  • Power-law distribution
  • Robust estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "A robust and efficient estimator for the tail index of inverse Pareto distribution",
abstract = "Based on the probability integral transform statistic, Finkelstein et al. (2006) have proposed a robust estimator for the shape parameter of Pareto distribution. In this paper, based on the same method, a robust and efficient estimator for the shape parameter of the inverse Pareto distribution is developed assuming that the threshold parameter is known. To study the robustness properties of this new estimator, we derive the asymptotic variance, breakdown point and gross error sensitivity. However, since the inverse Pareto distribution is literally an inverse of the Pareto distribution, some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by Finkelstein et al. (2006). The performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study. For the application, an inverse Pareto distribution is fitted to the lower tail data of Malaysian household incomes for the year of 2014, involving the proposed estimator in order to allow for the presence of outliers. Based on the inverse Pareto model, the parametric Lorenz curve is fitted and the Gini coefficient is estimated to measure the income inequality of poor households in Malaysia.",
keywords = "Inverse Pareto distribution, Inverse Pareto tail index, M-estimator, Power-law distribution, Robust estimation",
author = "Safari, {Muhammad Aslam Mohd} and Nurulkamal Masseran and Kamarulzaman Ibrahim and Hussain, {Saiful Izzuan}",
year = "2019",
month = "3",
day = "1",
doi = "10.1016/j.physa.2018.11.029",
language = "English",
volume = "517",
pages = "431--439",
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AU - Safari, Muhammad Aslam Mohd

AU - Masseran, Nurulkamal

AU - Ibrahim, Kamarulzaman

AU - Hussain, Saiful Izzuan

PY - 2019/3/1

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N2 - Based on the probability integral transform statistic, Finkelstein et al. (2006) have proposed a robust estimator for the shape parameter of Pareto distribution. In this paper, based on the same method, a robust and efficient estimator for the shape parameter of the inverse Pareto distribution is developed assuming that the threshold parameter is known. To study the robustness properties of this new estimator, we derive the asymptotic variance, breakdown point and gross error sensitivity. However, since the inverse Pareto distribution is literally an inverse of the Pareto distribution, some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by Finkelstein et al. (2006). The performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study. For the application, an inverse Pareto distribution is fitted to the lower tail data of Malaysian household incomes for the year of 2014, involving the proposed estimator in order to allow for the presence of outliers. Based on the inverse Pareto model, the parametric Lorenz curve is fitted and the Gini coefficient is estimated to measure the income inequality of poor households in Malaysia.

AB - Based on the probability integral transform statistic, Finkelstein et al. (2006) have proposed a robust estimator for the shape parameter of Pareto distribution. In this paper, based on the same method, a robust and efficient estimator for the shape parameter of the inverse Pareto distribution is developed assuming that the threshold parameter is known. To study the robustness properties of this new estimator, we derive the asymptotic variance, breakdown point and gross error sensitivity. However, since the inverse Pareto distribution is literally an inverse of the Pareto distribution, some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by Finkelstein et al. (2006). The performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study. For the application, an inverse Pareto distribution is fitted to the lower tail data of Malaysian household incomes for the year of 2014, involving the proposed estimator in order to allow for the presence of outliers. Based on the inverse Pareto model, the parametric Lorenz curve is fitted and the Gini coefficient is estimated to measure the income inequality of poor households in Malaysia.

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