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Unit-Modified Weibull Distribution and Quantile Regression Model

  • 0Federal University of Santa Maria, Roraima Avenue, 1000, 97105-900 Santa Maria, RS, Brazil.
Anais Da Academia Brasileira De Ciências +

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December 11, 2025

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December 11, 2025

View abstract on PubMed

Summary

This summary is machine-generated.

This study introduces a new unit probability distribution (UMW) for analyzing Sustainable Development Goals (SDG) data. The novel quantile regression model effectively analyzes SDG indicators and reading skills, supporting quality education and well-being.

Area Of Science

  • Statistics
  • Probability Theory
  • Sustainable Development

Background

  • Sustainable Development Goals (SDGs) require robust statistical methods for analysis.
  • Existing probability distributions may not adequately model data within the unit interval (0,1).
  • Modified Weibull (MW) distribution offers flexibility but needs adaptation for unit interval data.

Purpose Of The Study

  • To propose a new unit probability distribution, the Unit Modified Weibull (UMW) distribution.
  • To develop a quantile regression model for UMW distributed random variables.
  • To apply these methods to model SDG indicators and assess reading skills related to education and health.

Main Methods

  • Transformation of the modified Weibull distribution to create the UMW distribution.
  • Quantile regression model reparameterized for UMW distribution.
  • Maximum Likelihood Estimation (MLE) for parameter estimation and Monte Carlo simulations for evaluation.

Main Results

  • The UMW distribution is successfully derived and characterized.
  • The quantile regression model demonstrates effectiveness in parameter estimation.
  • Simulations confirm desirable properties of MLEs for UMW model parameters.
  • The methods are applied to real-world SDG indicators and dyslexia-related reading skills.

Conclusions

  • The UMW distribution and its associated quantile regression model provide a flexible framework for analyzing unit interval data.
  • These methods offer valuable tools for monitoring and evaluating progress towards Sustainable Development Goals.
  • The study highlights the interconnectedness of education, health, and sustainable development through data analysis.

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