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Representative Points of the Inverse Gaussian Distribution and Their Applications.

Wen-Wen Hu1, Kai-Tai Fang1,2, Xiao-Ling Peng1,3

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Summary
This summary is machine-generated.

This study introduces novel methods for approximating the inverse Gaussian (IG) distribution using representative points (RPs) and quantile estimators. Mean square error RPs and Harrell-Davis quantile estimators significantly improve statistical inference accuracy for IG distribution applications.

Keywords:
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Area of Science:

  • Statistics
  • Probability Theory
  • Data Analysis

Background:

  • The inverse Gaussian (IG) distribution is crucial in finance and reliability.
  • Accurate statistical inference for the IG distribution is essential for practical applications.
  • Existing methods for approximating discrete IG distributions have limitations.

Purpose of the Study:

  • To systematically investigate representative points (RPs) for discrete approximation of the IG distribution.
  • To introduce and evaluate advanced quantile estimators for enhanced IG distribution sampling.
  • To improve the accuracy and robustness of statistical inference for the IG distribution.

Main Methods:

  • Monte Carlo (MC-RPs), quasi-Monte Carlo (QMC-RPs), and mean square error RPs (MSE-RPs) were analyzed for IG distribution approximation.
  • The Harrell-Davis (HD) and Sfakianakis-Verginis (SV1, SV2, SV3) quantile estimators were applied.
  • Performance was evaluated through moment estimation, density approximation, resampling, and real-world case studies.

Main Results:

  • MSE-RPs demonstrated superior approximation accuracy and robustness compared to MC-RPs and QMC-RPs.
  • The HD and SV quantile estimators significantly improved the representativeness of IG distribution samples.
  • Parameter estimation accuracy was substantially enhanced by the proposed quantile estimators.

Conclusions:

  • MSE-RPs offer an efficient and robust method for discrete approximation of the IG distribution.
  • The use of HD and SV quantile estimators markedly improves IG distribution parameter estimation.
  • The proposed methodologies provide practical and effective tools for statistical inference involving the IG distribution.