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The beta Burr type X distribution properties with application.

Faton Merovci1, Mundher Abdullah Khaleel2, Noor Akma Ibrahim3

  • 1Department of Mathematics, Faculty of Natural Science and Mathematics, University of Mitrovica "Isa Boletini", Str. Industrial Park, 40000 Mitrovica, Republic of Kosovo.

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Summary
This summary is machine-generated.

Researchers introduced the beta-Burr type X distribution, a novel continuous model extending the Burr type X distribution. This new statistical model offers a flexible alternative for analyzing positive real-world data.

Keywords:
EstimationMomentOrder statisticsQuantile function

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • The Burr type X distribution is a recognized probability distribution.
  • Existing distributions may have limitations in modeling certain types of positive real data.
  • There is a continuous need for flexible statistical models in data analysis.

Purpose of the Study:

  • To introduce and mathematically characterize a new continuous distribution, the beta-Burr type X distribution.
  • To extend the properties of the existing Burr type X distribution.
  • To provide a flexible alternative for modeling positive real data.

Main Methods:

  • Derivation of key structural properties, including the moment generating function and rth moment.
  • Obtaining expressions for density, moment generating function, and rth moment of order statistics.
  • Parameter estimation using Maximum Likelihood Estimation (MLE).
  • Derivation of asymptotic confidence intervals using the Fisher information matrix.
  • Performance assessment through simulation studies and real data illustration.

Main Results:

  • The beta-Burr type X distribution was successfully developed and its mathematical properties were derived.
  • Generalizations of existing results in the literature were achieved.
  • The Maximum Likelihood Estimation method was applied for parameter estimation.
  • Asymptotic confidence intervals were computed.
  • Simulation studies demonstrated the model's performance across various sample sizes.

Conclusions:

  • The newly developed beta-Burr type X distribution provides a comprehensive mathematical framework.
  • The distribution serves as a viable and flexible alternative for modeling positive real data.
  • The study validates the utility of the beta-Burr type X distribution through empirical analysis.