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An extended approach for the generalized powered uniform distribution.

Carlos Rondero-Guerrero1, Isidro González-Hernández1, Carlos Soto-Campos1

  • 1Autonomous University of Hidalgo State, Mineral de la Reforma, Hidalgo Mexico.

Computational Statistics
|November 21, 2022
PubMed
Summary

A novel statistical model, the generalized powered uniform distribution (GPUD), offers enhanced flexibility for data analysis. This new distribution shows promise in modeling real-world datasets, including COVID-19 and cancer data.

Keywords:
COVID-19Generalized uniform distributionMaximum likelihood estimation

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • Existing uniform distribution models may lack the flexibility required for complex real-world data.
  • The need for adaptable statistical distributions in fields like epidemiology and medical research is growing.

Purpose of the Study:

  • Introduce a new flexible statistical model: the generalized powered uniform distribution (GPUD).
  • Generalize existing uniform distribution models, specifically the one by Jayakumar and Sankaran (2016).
  • Demonstrate the utility and flexibility of the GPUD using real-world datasets.

Main Methods:

  • Developed a new probability density function (pdf) incorporating a parameter 'k' and a powered mean operator.
  • Derived key statistical properties: shape characteristics of the pdf, higher-order moments, and moment generating function.
  • Applied the maximum likelihood method using the R 'maxLik' package for parameter estimation.

Main Results:

  • The proposed GPUD model demonstrated superior flexibility compared to other existing models.
  • The model successfully fitted real-world data from COVID-19 and bladder cancer studies.
  • Parameter estimation using the maximum likelihood method proved effective.

Conclusions:

  • The generalized powered uniform distribution (GPUD) is a flexible and valuable addition to statistical modeling.
  • The GPUD shows potential for application in diverse fields requiring robust data analysis.
  • The study validates the GPUD's performance on complex datasets.