Mathematical and Computational Applications

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.

In this study, a comprehensive analysis of the fixed/preassigned-time synchronization of a class of quaternion-valued BAM (QBAM) neural networks with stochastic and impulsive effects is conducted. Unlike previous analysis methods, our method features a direct analysis approach. First, to clarify the combined impact of impulsive and stochastic phenomena on synchronization behavior, we establish a QBAM neural network system incorporating stochastic and impulsive effects. Notably, differing from prior relevant studies, we assume that the activation function is discontinuous, thereby enhancing the practical relevance of this research. Second, leveraging the quaternion-valued sign function and its properties, we implement impulsive control via the direct analysis method to achieve Fixed/Predefined-Time synchronization of the considered system. Finally, numerical simulations are performed to verify the ability of the theoretical analysis and the proposed control protocol to realize synchronization under impulsive and stochastic effects.

Urban catchments are increasingly vulnerable to hydrologic extremes driven by land-use change and climate variability, challenging the traditional assumption of stationarity. This study develops a computational framework to assess the nonstationary behavior of peak flow, volume, and duration in an urban catchment in the Philippines using 39 years of daily flow records (June 1984–November 2022). Missing observations (~8% of the series) were reconstructed using multiple linear regression (MLR) and artificial neural networks (ANNs) with four predictors: daily rainfall, antecedent rainfall, antecedent flow, and built-up area index. MLR with all predictors yielded the most accurate reconstructions. Nonstationarity was detected using the Mann–Kendall test, Sen slope estimator, Pettitt test, and variance change test. Flood events were extracted using block maxima (BM) and peak-over-threshold (POT) methods. BM-based results showed stationary peak flow and volume, while duration increased by 1.78 h/year. POT analyses revealed nonstationarity across all variables, without significant shifts in variance. These findings demonstrate that methodological choices strongly influence nonstationary detection. The framework underscores the importance of reliable data reconstruction and robust statistical testing for nonstationary analysis of flood events. POT-based approaches more effectively capture evolving trends in peak flow, volume, and duration. These can be used in designing resilient infrastructure and flood risk management in urbanizing catchments.