Maximum likelihood estimation (MLE) of the four-parameter kappa distribution (K4D) is known to be occasionally unstable for small sample sizes and to be very sensitive to outliers. To overcome this problem, this study proposes Bayesian analysis of the K4D. Bayesian estimators are obtained by virtue of a posterior distribution using the random walk Metropolis–Hastings algorithm. Five different priors are considered. The properties of the Bayesian estimators are verified in a simulation study. The empirical Bayesian method turns out to work well. Our approach is then compared to the MLE and the method of the L-moments estimator by calculating the 20-year return level, the confidence interval, and various goodness-of-fit measures. It is also compared to modeling using the generalized extreme value distribution. We illustrate the usefulness of our approach in an application to the annual maximum wind speeds in Udon Thani, Thailand, and to the annual maximum sea-levels in Fremantle, Australia. In the latter example, non-stationarity is modeled through a trend in time on the location parameter. We conclude that Bayesian inference for K4D may be substantially useful for modeling extreme events.

This study aims to identify the optimal distribution for modeling extreme events based on annual maximum series data from meteorological stations in Southern Thailand. We explored three types of two-parameter Generalized Extreme Value (GEV) distributions—Weibull, Fréchet, and Gumbel—and compared their fit to the observed data using GEV. The fitting process involved estimating model parameters, for which we employed two mathematical techniques: least square estimation and maximum likelihood estimation. Our findings revealed that, when fitting GEV distribution with numerical estimation for the shape parameter, the Gumbel distribution, characterized by a light-tail, is the most suitable for nearly all stations. However, when considering the two-parameter case for the three distribution types, the Fréchet distribution, known for its heavy-tail, emerges as the best fit for many stations, exhibiting the lowest ratio mean square error.

A log beta generalized Weibull regression model was proposed by modification from beta generalized Weibull distribution. To predict the survival time, the maximum likelihood method was used to estimate parameters in the proposed regression model and then, the proposed regression model was applied with lifetime data. The Akaike information criterion, Bayesian information criterion and likelihood ratio statistic are criterion to compare the performance of the proposed regression model with sub models which are log beta Weibull regression model, log generalized Weibull regression and log Weibull regression model. The result showed that the proposed regression model performed better than the sub models.

Climate change has intensified the frequency and severity of extreme weather events, necessitating a nuanced understanding of flood patterns for effective risk management. This study examines flood risk in the Chi watershed, Thailand, using Weekly Moving Cumulative Rainfall (WMCR) data from 1990 to 2021. We employ extreme value copula analysis to assess spatial dependence between meteorological stations in the watershed. Nine bivariate generalized extreme value (BGEV) models were evaluated using the Akaike Information Criterion (AIC) and the Likelihood Ratio test (LRT) to ensure model robustness. The BGEV model revealed higher tail dependence among stations near the bay of the watershed. We also calculated the flood recurrence period to estimate flood events’ frequency and potential severity. Stations ST5 (Khon Kaen), ST6 (Tha Phra Khon Kaen), and ST8 (Maha Sarakham) were identified as potential hotspots, with higher probabilities of experiencing extreme rainfall of approximately 200 (mm.) during the rainy season. These findings provide valuable insights for flood management and mitigation strategies in the Chi watershed and offer a methodological framework adaptable to other regions facing similar challenges.

In this paper, a new discrete distribution named as the discrete odd inverse Pareto exponential (DOIPEx) distribution is introduced for modeling count data. The proposed distribution can be viewed as a generalization of the discrete Marshall-Olkin exponential, discrete exponentiate exponential, and discrete exponential distributions. Some basic distributional properties, quantile function, hazard and reversed hazard functions, and order statistics are derived. Estimation of the parameters is illustrated using the maximum likelihood method (MLE), and three real data sets are discussed to demonstrate the usefulness and applicability of the DOIPEx distribution.