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A novel two-parameter unit probability model with properties and applications.

Zawar Hussain1, Farrukh Jamal1, Abdus Saboor2

  • 1Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan.

Heliyon
|September 23, 2024
PubMed
Summary
This summary is machine-generated.

A new flexible two-parameter probability model, a generalized Kumaraswami distribution, offers superior data-fitting capabilities. This enhanced statistical tool demonstrates effectiveness across various real-world datasets.

Keywords:
60E0562E15Maximum likelihood methodNTPUP modelOrder statisticsSimulation analysis

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Area of Science:

  • Probability Theory
  • Statistical Modeling
  • Mathematical Statistics

Background:

  • Existing probability distributions often lack the flexibility to accurately model diverse real-world data.
  • The Kumaraswami distribution is a known statistical model, but generalizations can offer improved performance.

Purpose of the Study:

  • To introduce a novel two-parameter generalized Kumaraswami distribution.
  • To demonstrate the enhanced flexibility and applicability of this new distribution compared to existing models.

Main Methods:

  • Development of a novel two-parameter unit probability model.
  • Derivation of statistical properties including moments and order statistics.
  • Parameter estimation using maximum likelihood estimation (MLE).
  • Validation through numerical simulations and analysis of real data sets.

Main Results:

  • The proposed generalized Kumaraswami distribution exhibits greater flexibility due to unique hazard and density function shapes.
  • Explicit expressions for statistical measures like moments and order statistics were derived.
  • Maximum likelihood estimation proved consistent for parameter estimation.
  • The model effectively captured characteristics of four diverse real data sets.

Conclusions:

  • The novel two-parameter generalized Kumaraswami distribution is a flexible and effective statistical tool.
  • The model shows significant promise for analyzing diverse data across various scientific and applied fields.