A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications.

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Lifetime data analysis is crucial in various fields.
• Existing discrete lifetime distributions may lack flexibility.
• The Lindley distribution is a continuous model with limitations for discrete data.

Purpose of the Study:

• Introduce a novel two-parameter exponentiated discrete Lindley distribution.
• Investigate the comprehensive structural properties of the new distribution.
• Evaluate the performance of parameter estimation methods.

Main Methods:

• Derivation of key statistical properties: probability mass function, moments, skewness, kurtosis.
• Analysis of hazard rate function shapes (e.g., increasing, decreasing, bathtub, J-shaped).
• Estimation of model parameters using Maximum Likelihood and Proportion methods.
• Simulation study to assess bias and mean square error of estimators.
• Application to four real-world datasets to demonstrate flexibility.

Main Results:

• The proposed distribution exhibits diverse shapes for its probability mass and hazard rate functions.
• Maximum Likelihood and Proportion estimators show reliable performance in simulations.
• The new model demonstrates superior flexibility compared to existing lifetime distributions.
• The distribution effectively models positive real data across different application areas.

Conclusions:

• The two-parameter exponentiated discrete Lindley distribution offers a versatile alternative for lifetime data modeling.
• Its rich structural properties and reliable estimation methods make it valuable in statistical applications.
• The model's flexibility allows it to capture complex failure patterns effectively.