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Penalized likelihood approach for the four-parameter kappa distribution.

Nipada Papukdee1,2, Jeong-Soo Park3, Piyapatr Busababodhin1

  • 1Department of Mathematics, Mahasarakham University, Mahasarakham, Thailand.

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|June 16, 2022
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Summary
This summary is machine-generated.

This study introduces a new Maximum Penalized Likelihood Estimation (MPLE) for the four-parameter kappa distribution (K4D). MPLE improves parameter estimation, especially for small sample sizes in hydrology and climate change modeling.

Keywords:
Beta functionL-momentsextreme valueslikelihood-based inferencemeteorological dataquantile estimation

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Area of Science:

  • Statistics
  • Hydrology
  • Climatology

Background:

  • The four-parameter kappa distribution (K4D) is a flexible model used in hydrology and climate change.
  • Traditional estimation methods like L-moment estimators (LME) and maximum likelihood estimators (MLE) have limitations with moderate to small sample sizes.

Purpose of the Study:

  • To propose and evaluate a Maximum Penalized Likelihood Estimation (MPLE) for the K4D.
  • To improve the small sample properties of K4D parameter estimation.

Main Methods:

  • Developed MPLE by adjusting penalty functions to restrict the parameter space.
  • Compared eighteen combinations of penalties for the two shape parameters.
  • Validated the proposed estimator through Monte Carlo simulations.

Main Results:

  • MPLE demonstrates improved performance for small sample sizes compared to MLE.
  • The proposed method retains the flexibility and large-sample optimality of K4D.
  • Application to Thailand's annual maximum temperature data showcases practical utility.

Conclusions:

  • MPLE offers a robust alternative for estimating K4D parameters, particularly in scenarios with limited data.
  • The method enhances the reliability of K4D models in fields like hydrology and climate science.
  • This approach provides better statistical properties for parameter estimation in challenging data conditions.