A study on the new logarithmic-G family with statistical properties, simulations, and different data analysis

Area of Science:

• Probability Theory
• Statistical Modeling
• Data Analysis

Background:

• Traditional probability distributions inadequately model data with non-monotonic hazard rates.
• There is a need for enhanced statistical models to capture real-world data complexities.

Purpose of the Study:

• To introduce an innovative modeling technique using logarithmic functions for enhanced distribution adaptability.
• To define mathematical properties and estimation methods for the new model.
• To assess the performance of the proposed distribution against existing models.

Main Methods:

• Developed a new distribution incorporating logarithmic functions.
• Investigated and defined mathematical properties of the proposed methodology.
• Employed multiple estimation methods and conducted Monte Carlo simulations to evaluate parameter estimation (bias, MSE, MRE).

Main Results:

• The proposed New Log-Weibull (NLW) distribution demonstrated strong performance.
• Monte Carlo simulations validated the effectiveness of the estimation methods.
• The NLW distribution showed superior performance in analyzing COVID-19 and engineering datasets compared to alternatives.

Conclusions:

• The novel logarithmic distribution offers greater adaptability for complex datasets.
• The New Log-Weibull distribution is a promising tool for analyzing real-world data, including medical and engineering applications.
• The study validates the utility of enhanced probability distributions for non-monotonic hazard rate data.