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

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.