The Nadarajah-Haghighi Lindley distribution

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Lifetime models are crucial for analyzing the duration of systems or components.
• Existing models may have limitations in flexibility or applicability.
• The Lindley and Nadarajah-Haghighi distributions are established lifetime models.

Purpose of the Study:

• To introduce a new compound lifetime distribution.
• To investigate the mathematical properties of the proposed distribution.
• To assess the model's performance and applicability using real data.

Main Methods:

• Compounding the Lindley and Nadarajah-Haghighi distributions.
• Deriving mathematical properties: generating function, mean residual life, moments, Bonferroni and Lorenz curves, mean deviations.
• Parameter estimation using the maximum likelihood method.
• Empirical validation through simulation and real-data applications.

Main Results:

• The new compound distribution exhibits competitive performance compared to existing models.
• Key mathematical properties were derived and analyzed.
• Maximum likelihood estimation provided reliable parameter estimates.
• The model demonstrated a good fit to two real-world datasets.

Conclusions:

• The proposed compound lifetime distribution is a viable and useful alternative to classical models.
• The model's mathematical tractability and empirical performance support its adoption in reliability studies.
• Further research can explore extensions and applications of this new distribution.