• 대한수학회보
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• 제54권3호
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• pp.839-874
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• 2017

Our goal is to establish and prove the almost sure central limit theorems for some order statistics $\{M_n^{(k)}\}$, $k=1,2,{\ldots}$, formed by stochastic processes ($X_1,X_2,{\ldots},X_n$), $n{\in}N$, the distributions of which are defined by certain Archimedean copulas. Some properties of generators of such the copulas are intensively used in our proofs. The first class of theorems stated and proved in the paper concerns sequences of ordinary maxima $\{M_n\}$, the second class of the presented results and proofs applies for sequences of the second largest maxima $\{M_n^{(2)}\}$ and the third (and the last) part of our investigations is devoted to the proofs of the almost sure central limit theorems for the k-th largest maxima $\{M_n^{(k)}\}$ in general. The assumptions imposed in the first two of the mentioned groups of claims significantly differ from the conditions used in the last - the most general - case.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2022년도 학술발표회
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• pp.305-305
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• 2022

A better approach for assessing meteorological drought occurrences is increasingly important in mitigating and adapting to the impacts of climate change, as well as strategies for developing early warning systems. The present study defines meteorological droughts as a period with an abnormal precipitation deficit based on monthly precipitation data of 18 gauging stations for the Han River watershed in the past (1974-2015). This study utilizes a Bayesian parameter estimation approach to analyze the effects of climate change on future drought (2025-2065) in the Han River Basin using the Coupled Model Intercomparison Project Phase 6 (CMIP6) with four bias-corrected general circulation models (GCMs) under the Shared Socioeconomic Pathway (SSP)2-4.5 scenario. Given that drought is defined by several dependent variables, the evaluation of this phenomenon should be based on multivariate analysis. Two main characteristics of drought (severity and duration) were extracted from precipitation anomalies in the past and near-future periods using the copula function. Three parameters of the Archimedean family copulas, Frank, Clayton, and Gumbel copula, were selected to fit with drought severity and duration. The results reveal that the lower parts and middle of the Han River basin have faced severe drought conditions in the near future. Also, the bivariate analysis using copula showed that, according to both indicators, the study area would experience droughts with greater severity and duration in the future as compared with the historical period.