A New Lomax-G Family: Properties, Estimation and Applications.

Area of Science:

• Probability and Statistics
• Reliability Engineering
• Mathematical Modeling

Background:

• Increasing demand for advanced statistical distributions to interpret complex phenomena.
• Need for flexible models in reliability analysis and data modeling.

Purpose of the Study:

• Introduce a novel Lomax-G family of distributions based on the exponentiated reciprocal of the hazard rate.
• Investigate the properties and applications of the new Lomax-Weibull (NLW) distribution as a sub-model.
• Evaluate the performance of various parameter estimation techniques for the NLW distribution.

Main Methods:

• Derivation of cumulative and probability density functions for the new Lomax-G family.
• Analysis of the NLW distribution's density and hazard function shapes.
• Application of five estimation techniques: maximum likelihood, percentile, least squares, weighted least squares, and Cramér-von Mises.
• Comparative Monte Carlo simulation and real-world data validation.

Main Results:

• The NLW distribution exhibits diverse shapes (symmetric, skewed, inverted J) and asymmetric hazard functions.
• Simulation studies and numerical demonstrations assess the performance of estimation methods.
• The NLW distribution demonstrated a more accurate fit to real-world datasets compared to competing models.

Conclusions:

• The proposed Lomax-G family, particularly the NLW distribution, is a flexible and efficient tool for reliability analysis.
• The NLW distribution offers improved modeling capabilities for complex lifetime data.
• The study validates the effectiveness of the NLW distribution across various applications.