The power new XLindley distribution: Statistical inference, fuzzy reliability, and applications

Area of Science:

• Statistics
• Probability Distributions
• Mathematical Modeling

Background:

• The XLindley distribution is a valuable tool in statistical modeling.
• There is a continuous need for novel probability distributions with enhanced flexibility and applicability.

Purpose of the Study:

• To introduce and explore the properties of a new two-parameter distribution, the power new XLindley (PNXL) distribution.
• To assess the performance of PNXL distribution parameter estimators.
• To demonstrate the practical utility and superiority of the PNXL distribution using real-world data.

Main Methods:

• Derivation of the PNXL distribution using a power transformation method.
• Analytical exploration of key statistical properties (moments, MGF, survival/hazard functions, skewness, kurtosis).
• Development and evaluation of parameter estimation techniques via simulation studies.
• Model fitting and comparative analysis on real datasets.

Main Results:

• The structural properties of the PNXL distribution were thoroughly investigated.
• Parameter estimation methods were proposed and their performance evaluated.
• The PNXL distribution demonstrated superior performance compared to existing models on real datasets.

Conclusions:

• The power new XLindley (PNXL) distribution is a promising new statistical model.
• The PNXL distribution offers a robust and effective tool for data modeling and analysis.
• The study validates the PNXL distribution's applicability and advantages in practical scenarios.