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Inverse power XLindley distribution with statistical inference and applications to engineering data
Amal S Hassan1, Najwan Alsadat2, Christophe Chesneau3
1Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza, 12613, Egypt.
Scientific Reports
|February 5, 2025
Summary
A new inverse power XLindley distribution is introduced for modeling lifetime data, offering flexible probability density and hazard rate functions. The maximum product of spacing method proved most accurate for parameter estimation.
Area of Science:
- Statistics
- Probability Theory
- Reliability Engineering
Background:
- The power XLindley distribution is a flexible model for lifetime data.
- New distributions are needed to capture diverse data patterns in reliability and survival analysis.
Purpose of the Study:
- To introduce and analyze the novel inverse power XLindley distribution.
- To investigate its statistical properties and estimation methods for modeling lifetime phenomena.
Main Methods:
- Construction of the new distribution via inverse transformation technique.
- Derivation of mathematical properties including quantiles, moments, and inequality measures.
- Exploration of parameter estimation using twelve distinct methods, including maximum likelihood and maximum product of spacing.
Main Results:
- The inverse power XLindley distribution can generate symmetric and asymmetric probability density functions.
- Its hazard rate function exhibits increasing, decreasing, reverse J-shape, or J-shape.
- Monte Carlo simulations indicated the maximum product of spacing method offers superior accuracy and precision.
- The distribution's effectiveness was validated on three real-world datasets.
Conclusions:
- The proposed inverse power XLindley distribution is a versatile and effective tool for modeling various lifetime data.
- The maximum product of spacing estimation method is recommended for parameter estimation.
- The distribution's flexibility makes it a valuable addition to statistical modeling techniques.
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