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Inflated Kumaraswamy distributions.

Francisco Cribari-Neto1, Jéssica Santos1

  • 1Departamento de Estatística, Universidade Federal de Pernambuco, Av. Prof Luiz Freire, s/n, Cidade Universitária, 50670-901 Recife, PE, Brazil.

Anais Da Academia Brasileira De Ciencias
|May 30, 2019
PubMed
Summary

This study introduces inflated Kumaraswamy distributions to model data including zeros and ones. These new distributions offer flexibility for statistical modeling on the unit interval, addressing limitations of the standard Kumaraswamy distribution.

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • The standard Kumaraswamy distribution models data within the (0, 1) interval.
  • Real-world data often includes boundary values (0 or 1), necessitating distributions for [0, 1), (0, 1], or [0, 1] intervals.

Purpose of the Study:

  • To introduce novel inflated Kumaraswamy distributions.
  • To extend the applicability of Kumaraswamy distributions to datasets with boundary values.

Main Methods:

  • Development of inflated Kumaraswamy distributions with inflation at one or both endpoints.
  • Parameter estimation techniques including point and interval estimation.
  • Hypothesis testing procedures for model inference.

Main Results:

  • Introduction of inflated Kumaraswamy distributions for modeling data on the unit interval, including boundary values.
  • Detailed discussion of the properties of these new distributions.
  • Monte Carlo simulations assessing the finite sample performance of estimation and hypothesis testing.

Conclusions:

  • Inflated Kumaraswamy distributions provide a robust framework for statistical modeling of data on the unit interval, accommodating boundary values.
  • The proposed methods for parameter estimation and hypothesis testing are validated through simulation studies.
  • An empirical application demonstrates the practical utility of the inflated Kumaraswamy distributions.