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The cosine geometric distribution with count data modeling.

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Summary
This summary is machine-generated.

A new trigonometric weighted geometric distribution is introduced for analyzing over-dispersed data. This novel discrete distribution offers an oscillating property, outperforming existing models in practical applications.

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60E0562E15Weighted geometric distributioncumulative distribution functiondata with over-dispersion

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • The standard geometric distribution (GD) is a fundamental discrete probability distribution.
  • Over-dispersion in data presents challenges for standard statistical models.
  • Weighted geometric distributions offer flexibility but may lack specific properties for certain data types.

Purpose of the Study:

  • Introduce a novel two-parameter discrete distribution based on the weighted geometric distribution.
  • Incorporate a trigonometric weight to impart an oscillating property.
  • Develop a distribution suitable for analyzing over-dispersed data.

Main Methods:

  • Derivation of the cumulative distribution function, hazard rate function, and moment generating function.
  • Parameter estimation using the maximum likelihood method.
  • Simulation studies to assess estimator convergence.

Main Results:

  • The new distribution exhibits an oscillating property due to the trigonometric weight.
  • Maximum likelihood estimation provides reliable parameter estimates, as shown by simulations.
  • The proposed model demonstrates competitive or superior performance compared to existing distributions on practical datasets.

Conclusions:

  • The introduced trigonometric weighted geometric distribution is a valuable addition to the statistical toolkit.
  • The oscillating property makes it particularly useful for over-dispersed data.
  • Empirical applications confirm the model's efficacy and robustness.