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On the Extended Generalized Inverted Kumaraswamy Distribution.

Qasim Ramzan1, Sadia Qamar1, Muhammad Amin1

  • 1Department of Statistics, University of Sargodha, Sargodha, Pakistan.

Computational Intelligence and Neuroscience
|February 28, 2022
PubMed
Summary

Researchers introduce a new statistical model, the extended generalized inverted Kumaraswamy generated (EGIKw-G) family, for analyzing lifetime data. This flexible model, including the EGIKw-Burr XII, shows superior performance in real-world applications.

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • The development of flexible statistical distributions is crucial for accurately modeling complex data.
  • Existing generalized distributions may not capture the full range of behaviors observed in lifetime data.

Purpose of the Study:

  • To introduce a novel, flexible class of probability distributions: the extended generalized inverted Kumaraswamy generated (EGIKw-G) family.
  • To derive and analyze the key structural properties of this new distribution family.
  • To demonstrate the utility and superiority of a specific model within this family (EGIKw-Burr XII) for lifetime data analysis.

Main Methods:

  • Mathematical derivation of structural properties including survival function, hazard rate function, quantile function, and moments.
  • Parameter estimation using the maximum likelihood estimation (MLE) method.
  • Model performance evaluation through Monte Carlo simulations (MCS).

Main Results:

  • The EGIKw-G family of distributions is mathematically defined and its properties are derived.
  • The extended generalized inverted Kumaraswamy Burr XII (EGIKw-Burr XII) model is presented as a key special case.
  • Simulation studies and real-world data application confirm the effectiveness and superiority of the EGIKw-Burr XII model.

Conclusions:

  • The proposed EGIKw-G family offers a valuable addition to the toolkit of statistical distributions.
  • The EGIKw-Burr XII model demonstrates strong performance in modeling lifetime data, outperforming existing models.
  • This research provides a robust framework for statistical modeling in various applied fields.