What question did this study set out to answer?

The aim is to introduce and evaluate the Square New XLindley distribution for modeling positively skewed data.

March 23, 2026Open Access

Square New XLindley Distribution:Statistical Properties, Numerical Simulations and Applications in Sciences

Key Points

The aim is to introduce and evaluate the Square New XLindley distribution for modeling positively skewed data.
Introduced the SNXL distribution using square transformation of the NXL model.
Derived statistical properties including moments and quantile functions.
Estimated parameters using maximum likelihood estimation, maximum product of spacings estimation, and weighted least squares estimation.
Conducted Monte Carlo simulations to assess estimator performance.
Applied the SNXL distribution to real engineering and biomedical datasets.
The SNXL distribution shows superior fit in modeling lifetime data compared to classical models.
Statistical properties indicate strong analytical tractability and utility in applications.
Monte Carlo studies demonstrate low bias and mean squared error for estimators.

Abstract

In this paper, a new one-parameter lifetime distribution, called the Square New XLindley (SNXL) distribution, is proposed using a square transformation of the New XLindley (NXL) model. The motivation for introducing the SNXL model is to obtain a parsimonious distribution capable of modeling positively skewed data with an increasing failure rate, a common feature in reliability and materials strength applications, while retaining analytical tractability. Several statistical properties of the SNXL distribution are derived, including moments, quantile function, incomplete moments, stochastic ordering, actuarial measures, and fuzzy reliability characteristics.Parameter estimation is investigated using maximum likelihood estimation (MLE), maximum product of spacings estimation (MPSE), and weighted least squares estimation (WLSE). A Monte Carlo simulation study is conducted to evaluate the finite-sample performance of these estimators in terms of bias, mean squared error, and mean relative error. The practical usefulness of the SNXL distribution is illustrated using real engineering and biomedical datasets and compared with several competing Lindley-type and classical lifetime models. Graphical diagnostics, formalgoodness-of-fit tests, and information criteria indicate that the SNXL model provides a superior or competitive fit while maintaining model simplicity. These results suggest that the SNXL distribution is a useful alternative formodeling lifetime data characterized by monotone hazard rates.

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