Confidence interval estimation of the shape parameter of pareto distribution using extreme order statistics

Research output: Contribution to journalArticle

Abstract

The asymptotic distributions of several estimators of the shape parameter α of the Pareto distribution in the case where the scale parameter is known are derived. The study is carried out using simple random sampling (SRS), extreme ranked set sampling (ERSS) and on random samples that are based on minimum order statistics only or maximum order statistics only. These distributions are used to construct asymptotic confidence intervals (ACI) for α. A simulation study then compares these confidence intervals via their expected lengths and coverage probabilities.

Original languageEnglish
Pages (from-to)4627-4640
Number of pages14
JournalApplied Mathematical Sciences
Volume6
Issue number93-96
Publication statusPublished - 2012

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Extreme Order Statistics
Pareto Distribution
Interval Estimation
Shape Parameter
Order Statistics
Confidence interval
Statistics
Sampling
Ranked Set Sampling
Expected Length
Simple Random Sampling
Coverage Probability
Scale Parameter
Asymptotic distribution
Extremes
Simulation Study
Estimator

Keywords

  • Asymptotic confidence interval
  • Coverage probability
  • Expected length
  • Extreme ranked set sampling
  • Maximum order statistics
  • Minimum order statistics
  • Pareto distribution
  • Shape parameter
  • Simple random sampling

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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abstract = "The asymptotic distributions of several estimators of the shape parameter α of the Pareto distribution in the case where the scale parameter is known are derived. The study is carried out using simple random sampling (SRS), extreme ranked set sampling (ERSS) and on random samples that are based on minimum order statistics only or maximum order statistics only. These distributions are used to construct asymptotic confidence intervals (ACI) for α. A simulation study then compares these confidence intervals via their expected lengths and coverage probabilities.",
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