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In this work, we present the implementation of the Unit Maxwell-Boltzmann (UMB) distribution within the gamlss package in R, specifically included in the ZeroOneDists package, providing users with a flexible and robust tool for statistical modeling. This implementation enables the computation of probabilities, quantiles, and random numbers, as well as parameter estimation and the development of regression models within the gamlss framework. To evaluate its performance, we conducted a comprehensive simulation study comparing the UMB distribution with other commonly used distributions. The results highlight the effectiveness of the UMB distribution in capturing data variability and improving model accuracy. This contribution extends the capabilities of the gamlss package, offering R users an advanced resource for data analysis and regression modeling, especially in contexts where flexibility and precision are crucial.

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Implementation and Applications of the Unit Maxwell-Boltzmann Distribution in the Gamlss Framework for Environmental Data Analysis

  • 会议论文

  • 发表日期：

    2026年

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  • David Villegas Ceballos,
  • Freddy Hernandez-Barajas,
  • Olga Cecilia Usuga-Manco

摘要

In this work, we present the implementation of the Unit Maxwell-Boltzmann (UMB) distribution within the gamlss package in R, specifically included in the ZeroOneDists package, providing users with a flexible and robust tool for statistical modeling. This implementation enables the computation of probabilities, quantiles, and random numbers, as well as parameter estimation and the development of regression models within the gamlss framework. To evaluate its performance, we conducted a comprehensive simulation study comparing the UMB distribution with other commonly used distributions. The results highlight the effectiveness of the UMB distribution in capturing data variability and improving model accuracy. This contribution extends the capabilities of the gamlss package, offering R users an advanced resource for data analysis and regression modeling, especially in contexts where flexibility and precision are crucial.