The four-parameter kappa distribution (K4D) is a generalized form of some commonly used distributions such as generalized logistic, generalized Pareto, generalized Gumbel, and generalized extreme value (GEV) distributions. Owing to its flexibility, the K4D is widely applied in modeling in several fields such as hydrology and climatic change. For the estimation of the four parameters, the maximum likelihood approach and the method of L-moments are usually employed. The L-moment estimator (LME) method works well for some parameter spaces, with up to a moderate sample size, but it is sometimes not feasible in terms of computing the appropriate estimates. Meanwhile, using the maximum likelihood estimator (MLE) with small sample sizes shows substantially poor performance in terms of a large variance of the estimator. We therefore propose a maximum penalized likelihood estimation (MPLE) of K4D by adjusting the existing penalty functions that restrict the parameter space. Eighteen combinations of penalties for two shape parameters are considered and compared. The MPLE retains modeling flexibility and large sample optimality while also improving on small sample properties. The properties of the proposed estimator are verified through a Monte Carlo simulation, and an application case is demonstrated taking Thailand’s annual maximum temperature data.

This study explores the effectiveness of cow bone char as a low-cost, eco-friendly, and biodegradable adsorbent for removing Cu(II) and Ni(II) ions from acidic wastewater as challenging is due to heavy metal-contaminated industrial wastewater. Batch adsorption experiments were conducted to evaluate performance, with advanced nonlinear kinetic and isotherm models applied to analyze the adsorption behavior. Model fitting was performed using Microsoft Excel Solver, and model selection was validated using the Akaike Information Criterion and Average Absolute Relative Deviation Percentage. The FL-PFO kinetic model provided the best fit for time-dependent data, while the Liu and Toth isotherm models most accurately described equilibrium adsorption. Maximum adsorption capacities were 110 mg g⁻¹ for Cu(II) and 95 mg g⁻¹ for Ni(II), with Cu(II) exhibiting faster and more complete removal. Reusability testing over five cycles showed good potential for repeated use, though with gradual efficiency decline due to structural degradation and limited site regeneration. These results confirm the suitability of cow bone char as a sustainable and effective adsorbent for heavy metal removal, particularly in low-resource or decentralized water treatment systems.

Parameter estimation strategies have long been a focal point in research due to their significant implications for understanding data behavior, including the dynamics of big data. This study offers an advancement in these strategies by proposing an adaptive parameter estimation approach for the Generalized Extreme Value distribution (GEVD) using an artificial neural network (ANN). Through the proposed adaptive parameter estimation approach, based on ANNs, this study addresses the parameter estimation challenges associated with the GEVD. By harnessing the power of ANNs, the proposed methodology provides an innovative and effective solution for estimating the parameters of the GEVD, enhancing our understanding of extreme value analysis. To predict the flood risk areas in the Chi river watershed in Thailand, we first determine the variables that are significant in estimation of the three GEVD parameters $\mu ,\sigma$, and $\xi$ by considering the respective correlation coefficient and then estimating these parameters. The data were compiled from satellite and meteorological data in the Chi watershed gathered from the Meteorological Department and 92 meteorological stations from 2010 to 2021, and consist of such variables as the Normalized Difference Vegetation Index (NDVI), climate, rainfall, runoff, and so on. The parameter estimation focuses on the GEVD. Taking into consideration that the processes could be stationary (parameters are constant over time, S) or non-stationary (parameters change over time, NS), maximum likelihood estimation and ANN approaches are applied, respectively. Both cases are modeled with the GEVD for the monthly maximum rainfall. The Nash-Sutcliffe coefficient (NSE), is used to compare the performance and accuracy of the models. The results illustrate that the non-stationary model was suitable for 82 stations, while the stationary model was suitable for only 10 stations. The NSE values in each model range from 0.6 to 0.9. This indicated that all 92 models were highly accurate. Furthermore, it is found that meteorological variables, geographical coordinates, and NDVI, that are correlated with the shape parameter in the ANN model, are more significant than others. Finally, two-dimensional maps of the return levels in the 2, 5, 10, 20, 50, and 100-year return periods are presented for further application. Overall, this study contributes to the advancement of parameter estimation strategies in the context of extreme value analysis and offers practical implications for water resource management and flood risk mitigation.

The generalized extreme value (GEV) distribution is used to model block maxima and extrapolate beyond the observed range, making adequate tail fit essential. We propose a bounded, tunable goodness-of-fit statistic for the GEV distribution with unknown parameters, based on the probability integral transform and a symmetric weight whose amplitude and concentration are controlled separately. We establish location–scale invariance, an exact relationship with the Cramér–von Mises statistic, a known-parameter limit distribution with closed-form moments, consistency against fixed alternatives, and a composite-null limit conditional on explicit regularity assumptions. Critical values are obtained by a parametric bootstrap that refits the GEV model in every resample; the same calibration is applied to the Kolmogorov–Smirnov, Anderson–Darling, Cramér–von Mises, and upper-tail modified Anderson–Darling tests. Simulations over shape parameters from $-0.4$ to $0.4$ and sample sizes from 15 to 100 show no evidence of over-rejection, and the proposed tests are competitive with Anderson–Darling under maximum-likelihood and probability-weighted-moment estimation. All six tests have limited power against subtle upper-tail-only departures. The return-level study shows that rejection can identify samples with greater extrapolation error, whereas non-rejection does not guarantee accurate remote-quantile estimates. Applications to environmental and actuarial block maxima illustrate sensitivity to temporal trend and block length.