On a new generalized lindley distribution: Properties, estimation and applications

Area of Science:

• Statistics
• Probability Theory
• Survival Analysis

Background:

• The generalized Lindley distribution is a known model for lifetime data.
• Existing models may lack the flexibility required for complex survival data.
• The Marshall-Olkin method offers a way to generate new, flexible distributions.

Purpose of the Study:

• To introduce a new flexible statistical distribution for survival and lifetime data modeling.
• To develop and analyze the properties of this extended generalized Lindley distribution.
• To demonstrate its practical utility through real-world data analysis.

Main Methods:

• Extension of the generalized Lindley distribution using the Marshall-Olkin method.
• Derivation of statistical properties and reliability analysis.
• Estimation of model parameters using Maximum Likelihood Estimation (MLE).
• Simulation study to evaluate estimator efficiency using Mean Squared Error (MSE).

Main Results:

• The proposed extended generalized Lindley distribution demonstrates significant flexibility.
• Statistical properties and characterizations of the new distribution were derived.
• Maximum likelihood estimators and asymptotic variance-covariance matrix were obtained.
• Simulation results indicated the efficiency of the proposed estimators.
• The new model provided a superior fit to a real data set compared to other distributions.

Conclusions:

• The extended generalized Lindley distribution is a flexible and viable alternative for survival and lifetime data analysis.
• The developed statistical inference methods are effective for parameter estimation.
• The model's performance on real data confirms its practical applicability and superiority over competing models.