The Topp-Leone Generalized Inverted Exponential Distribution with Real Data Applications

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Lifetime data analysis is crucial in various fields.
• Existing lifetime models may not capture complex data patterns effectively.
• Development of new flexible statistical distributions is an ongoing research area.

Purpose of the Study:

• To introduce a novel three-parameter lifetime model: the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution.
• To derive key statistical properties of the proposed TLGIE distribution.
• To assess the performance of the TLGIE distribution using real-world data.

Main Methods:

• Introduction of the TLGIE distribution.
• Derivation of mathematical properties: moments, quantile function, survival function, hazard rate function, mean deviation, and mode.
• Parameter estimation using the Maximum Likelihood Estimation (MLE) method.
• Analysis of the Fisher Information Matrix for estimator properties.

Main Results:

• The TLGIE distribution is mathematically defined and its properties are derived.
• Maximum likelihood estimators for the TLGIE parameters are obtained.
• The performance and applicability of the TLGIE model are demonstrated through three real data set applications.

Conclusions:

• The proposed TLGIE distribution offers a new flexible tool for lifetime data analysis.
• The derived properties and estimation methods provide a solid foundation for its use.
• Empirical results confirm the utility of the TLGIE distribution in practical scenarios.