Year: 2025
Type: article
Abstract: In many fields, including engineering, biology and economics, modeling and analyzing lifetime data is crucial for understanding the reliability and survival characteristics of systems and components. To address the limitations of existing lifetime distributions in capturing complex hazard rate behaviors, this article introduces a new and flexible two-parameter distribution, the power length-biased XLindley (PLXL) distribution. This distribution extends the XLindley distribution family by incorporating a power transformation applied to a length-biased variant, thereby enriching its structural flexibility. It can model a variety of hazard rate shapes, including increasing, decreasing, decreasing–increasing–decreasing and inverted bathtub forms, making it suitable for a range of real-world applications. We derive the statistical properties of the PLXL distribution and develop parameter estimation methods based on the maximum likelihood and the least squares approach. We conduct a comprehensive simulation study to evaluate the performance of the proposed estimators in terms of bias and mean squared error. The practical utility and superior adaptability of the PLXL distribution are demonstrated by applying it to real lifetime data sets.
DOI: 10.3390/mca31010004
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,689
OpenAlex ID: W7117134638