A New Truncated Lindley-Generated Family of Distributions: Properties, Regression Analysis, and Applications

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The need for flexible probability distributions in statistical modeling.
• Limitations of existing distributions in capturing complex data patterns.

Purpose of the Study:

• Introduce the novel truncated Lindley-G (TLG) distribution.
• Analyze the mathematical properties and characteristics of the TLG model.
• Develop and evaluate a regression model based on the TLG distribution.

Main Methods:

• Composition of a truncated Lindley distribution with a parent distribution G(x).
• Derivation of critical points, moments, generating function, quantile function, mean deviations, and entropy.
• Parameter estimation using the maximum likelihood method.
• Simulation studies to assess estimator behavior under various conditions.
• Application to four real-world datasets.

Main Results:

• The TLG model offers an additional shape parameter for enhanced flexibility.
• The study details key mathematical properties of the TLG distribution.
• A regression model based on the truncated Lindley-Weibull distribution is proposed.
• Simulation results provide insights into the performance of parameter estimators.
• Real data analysis demonstrates the practical utility of the TLG model.

Conclusions:

• The TLG model is a valuable addition to the family of probability distributions.
• The proposed regression model shows potential for analyzing complex data.
• The study validates the model's performance through simulations and real-world applications.