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Frequency analysis is a widely used method in hydrology; however, the conventional approaches to frequency analysis do not consider the spatial dependence between stations. This study proposes a novel approach for multisite frequency analysis using the copula method. This approach uses the framework of pair copula construction to extended bivariate copula functions for multivariate analysis, allowing for non-homogeneous marginal distribution and spatial dependence. Our approach was applied to analyze hourly rainfall in Taiwan's Lanyang watershed from 1996 to 2011, constructing the multisite rainfall distribution to estimate the frequency of extreme rainfall events. The results showed the nonlinear relationships and distinct frequency distributions of rainfall across the study area due to changes in elevations. Based on the copula-based multisite rainfall distribution, the study simulated extreme rainfall events at multiple sites with predetermined frequencies, preserving the spatial characteristics of rainfall more accurately than previous methods. This approach avoids potential underestimation and overestimation of hourly rainfall intensity at specified return periods resulting from assumptions of homogeneity and spatial independence. This study also evaluated possible multisite rainfall combinations at a given frequency using Monte-Carlo simulation. These simulations characterized spatial uncertainties in design multisite rainfall, providing critical information for water resources management and hydrological design. [ABSTRACT FROM AUTHOR]

The copula is well-known for learning scale-free measures of dependence among variables and has invited much interest in recent years. At the very coronary heart of the copula, the concept is the well-known theorem of Sklar. It states that any multivariate distribution function can be disintegrated into the marginal distributions and a copula, which comprises the reliance between variables. On the other hand, the decision tree is a renowned nonparametric dominant modeling approach used for both regression and labeling problems. A decision tree represents a tree-structured classification of the data into surprising instructions for simplicity and prediction reason. In this paper, we are going to appraise with novel nonparametric copula-based decision tree organization using a measure of dependence: maximal information coefficient as classification index for two related variables which best classify the data concerning looking at the factors, but additionally ranked the factors in line with their inferences. Additionally, we pre-test the splitting criteria value to anticipate growing branches of the decision tree at each infant node. For example, we followed our proposed method to credit card records for Taiwan and coronary heart disease records of Pakistan and acquired the desirable outcomes. As a result, the anticipated method of initiating two-variable decision trees is tested using constructive tools for classification, prediction and reconnecting critical factors in statistics, finance, fitness sciences, machine learning, and many other associated fields. [ABSTRACT FROM AUTHOR]

This study aims to model the joint drought duration and severity distribution using two-dimensional copulas. The method of inference function for margins (IFM method) is employed to construct copulas. Two separate maximum likelihood estimations of univariate marginal distributions are performed first, then followed by a maximization of the bivariate likelihood as a function of the dependence parameters. The drought duration and severity are assumed to be exponential and gamma distributions, respectively. Several copulas are tested to determine the best data fitted copula. Droughts, defined using the Standardized Precipitation Index (SPI), of Wushantou (Taiwan) are employed as an example to illustrate the proposed methodology. The copula fitting results for drought duration and severity are quite satisfactory. The bivariate drought analyses, including the joint probabilities and bivariate return periods, based on the derived copula-based joint distribution are also investigated to demonstrate the advantages of bivariate modeling of droughts. [ABSTRACT FROM AUTHOR]