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A one-parameter discrete distribution for over-dispersed data: statistical and reliability properties with

M S Eliwa1,2, M El-Morshedy3,2

  • 1Misr Higher Institute for Commerce and Computers, Science and Technology Academy, Mansoura, Egypt.

Journal of Applied Statistics
|June 27, 2022
PubMed
Summary

A new flexible discrete distribution is proposed to model complex real-world data. This one-parameter model effectively captures over-dispersed, skewed, and leptokurtic datasets, offering an alternative to existing discrete distributions.

Keywords:
60E0562E1062F1062N05Discrete distributionestimation methodshazard rate functionsimulation

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Area of Science:

  • Statistics
  • Probability Theory
  • Distribution Theory

Background:

  • Existing discrete distributions struggle with complex, modern data.
  • The need for flexible models in distribution theory is growing.
  • Technological advancements generate increasingly complex datasets.

Purpose of the Study:

  • Introduce a novel, flexible one-parameter discrete distribution.
  • Derive key statistical and reliability properties of the new model.
  • Demonstrate the model's versatility in analyzing diverse real-world data.

Main Methods:

  • Development of a new one-parameter discrete distribution.
  • Derivation of closed-form statistical and reliability properties.
  • Estimation of model parameters using various approaches.
  • Simulation study to assess estimator performance.
  • Application to four real-world datasets from different fields.

Main Results:

  • The proposed distribution exhibits flexibility in modeling over-dispersed, positively skewed, and leptokurtic data.
  • It effectively models increasing, decreasing, and unimodal failure rates.
  • Simulation results confirm the performance of parameter estimators across different sample sizes.
  • Analysis of real data demonstrates the model's practical applicability.

Conclusions:

  • The new discrete distribution offers a flexible and effective alternative for modeling positive real data.
  • Its ability to handle complex data characteristics makes it valuable in various application areas.
  • The derived properties and demonstrated applications support its utility in statistical modeling.