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New bounded unit Weibull model: Applications with quantile regression.

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This summary is machine-generated.

This study introduces a novel bounded probability distribution for data between 0 and 1. The new Weibull-transformed model and its regression applications show superior performance in risk assessment and education.

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Area of Science:

  • Statistics
  • Probability Theory
  • Data Modeling

Background:

  • Ratios and proportions (0-1 range) present unique statistical modeling challenges.
  • Existing distributions like beta and Kumaraswamy have limitations.
  • Need for advanced models for bounded data analysis.

Purpose of the Study:

  • Introduce a new bounded probability distribution derived from the Weibull distribution.
  • Develop statistical tools, including the sequential probability ratio test (SPRT), for the proposed model.
  • Evaluate the model's performance in quantile regression for real-world applications.

Main Methods:

  • Transformation of the Weibull distribution to create a new bounded distribution.
  • Derivation of moments, entropies, and quantile function.
  • Parameter estimation using maximum likelihood estimation (MLE).
  • Monte Carlo simulations for performance evaluation.
  • Quantile regression modeling.

Main Results:

  • The proposed bounded distribution offers a flexible alternative for modeling data in the [0, 1] interval.
  • Maximum likelihood estimation effectively estimates model parameters.
  • The quantile regression model demonstrated superior performance compared to alternatives in risk assessment and educational attainment datasets.

Conclusions:

  • The new Weibull-transformed bounded distribution enhances the statistical toolkit for analyzing bounded variables.
  • The proposed model and its regression framework offer improved analytical capabilities across scientific fields.
  • Highlights the importance of developing specialized distributions for specific data ranges.