Lomax exponential distribution with an application to real-life data.

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The Lomax distribution is a widely used model for lifetime data.
• Existing modifications may lack flexibility in capturing diverse failure patterns.
• There is a need for more adaptable statistical distributions in reliability analysis.

Purpose of the Study:

• Introduce a novel Lomax exponential (LE) distribution.
• Investigate its mathematical properties and parameter estimation.
• Evaluate its performance against other Lomax-based models using real-world data.

Main Methods:

• Derivation of analytical expressions for key statistical properties (incomplete moments, quantile function, order statistics).
• Application of Maximum Likelihood Estimation (MLE) for parameter estimation.
• Assessment of model fit using standard metrics (AIC, CAIC, BIC, HQIC) and comparison with competing distributions.

Main Results:

• The Lomax exponential distribution demonstrates flexibility in modeling non-monotonic lifetime data (both decreasing and increasing failure rates).
• Explicit formulas for various statistical measures and Renyi entropy were derived.
• Parameter estimation via MLE was successfully implemented and validated on two real datasets.

Conclusions:

• The proposed Lomax exponential distribution is a superior and more flexible alternative for lifetime data analysis compared to Lomax, Weibull Lomax, and exponential Lomax distributions.
• The model's performance is robust, as indicated by goodness-of-fit measures.
• The LE distribution offers a valuable tool for reliability and survival analysis.