Maximum Likelihood Estimation Methods for Copula Models

Zhang, Jinyu; Gao, Kang; Li, Yong; Zhang, Qiaosen

doi:10.1007/s10614-021-10139-0

Cited by 9 publications

(3 citation statements)

References 31 publications

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“…Parameter θ for each copula is estimated by applying maximum likelihood estimation method (MLE) (Ko & Hjort, 2019; Weiß, 2011; J. Zhang et al., 2022) and estimated values are evaluated whether they are in a valid range. The parameter θ for the Clayton copula must be defined in [−1, ∞], except for zero, while the valid range for the Gumbel‐Hougaard and Joe copula is [1, ∞].…”

Section: Methodsmentioning

confidence: 99%

A Multivariate Frequency Analysis Framework to Estimate the Return Period of Hurricane Events Using Event‐Based Copula

Cho,

Ahmadisharaf,

Done

et al. 2023

Water Resources Research

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This study proposed a framework to evaluate multivariate return periods of hurricanes using event‐based frequency analysis techniques. The applicability of the proposed framework was demonstrated using point‐based and spatial analyses on a recent catastrophic event, Hurricane Ian. Univariate, bivariate, and trivariate frequency analyses were performed by applying generalized extreme value distribution and copula on annual maximum series of flood volume, peak discharge, total rainfall depth, maximum wind speed, wave height and storm surge. As a result of point‐based analyses, return periods of Hurricane Ian was investigated by using our framework; univariate return periods were estimated from 39.2 to 60.2 years, bivariate from 824.1 to 1,592.6 years, and trivariate from 332.1 to 1,722.9 years for the Daytona‐St. Augustine Basin. In the Florida Bay‐Florida Keys Basin, univariate return periods were calculated from 7.5 to 32.9 years, bivariate from 36.5 to 114.9 years, and trivariate from 25.0 to 214.8 years. Using the spatial analyses, we were able to generate the return period map of Hurricane Ian across Florida. Based on bivariate frequency analyses, 18% of hydrologic unit code 8 (HUC8) basins had an average return period of more than 30 years. Sources of uncertainty, due to the scarcity of analysis data, stationarity assumption and impact of other weather systems such as strong frontal passages, were also discussed. Despite these limitations, our framework and results will be valuable in disaster response and recovery.

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Section: Methodsmentioning

confidence: 99%

A Multivariate Frequency Analysis Framework to Estimate the Return Period of Hurricane Events Using Event‐Based Copula

Cho,

Ahmadisharaf,

Done

et al. 2023

Water Resources Research

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“…The marginal distribution functions u = F 1 (t) and v = F 2 (t) for frequency and amplitude are used as input values in the Copula function. The Copula function parameters θ are then calculated using the maximum likelihood estimation method [19].…”

Section: Modeling With Two Correlated Degradation Featuresmentioning

confidence: 99%

Performance Degradation Modeling and Continuous Worktime Assessment of Ultrasonic Vibration Systems

Wang,

You,

2024

Processes

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In order to assess the stable operating duration of an ultrasonic vibration system, a reliability-based analysis method for the stability of the ultrasonic vibration system is proposed. Firstly, the failure mechanisms of the ultrasonic vibration system are analyzed, and the resonant frequency and amplitude are selected as two degradation features of the system. Subsequently, accelerated degradation experiments under different force loads were conducted, and the degradation model of the ultrasonic vibration system was established by comparing experimental data with degradation, distribution, and acceleration models. Finally, Copula functions were introduced to connect the two degradation features, resonant frequency, and amplitude, and lifetime curves were plotted under the influence of univariate and bivariate degradation factors. Through the analysis of the lifetime curves, the conclusion is drawn that the decay of amplitude is the primary indicator of system lifetime, and it is predicted that the developed ultrasonic vibration system can operate continuously and stably for 26.69 h. This research is of great significance for enhancing the reliability and lifespan management of ultrasonic vibration systems.

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“…where x is the statistical parameters, such as drought duration, drought severity; α, β, and a 0 are the distribution parameters by using the maximum-likelihood method [27].…”

Section: Copula Function For Drought Frequency and Return Periodmentioning

confidence: 99%

A New Agricultural Drought Disaster Risk Assessment Framework: Coupled a Copula Function to Select Return Periods and the Jensen Model to Calculate Yield Loss

Liu

Pan

et al. 2023

Sustainability

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China is one of the regions with the most frequent drought disasters and serious social and economic losses. Agricultural drought loss is one the most serious natural disasters. Due to climate change, the regional agricultural drought risk assessment has always been the focus of the academic circle. This study takes Zunyi City as an example, which is the most typical City of karst landform development. The monthly precipitation data set of ground meteorological observation stations in Zunyi City from 1956 to 2020 was selected, and the drought characteristic variables were extracted by the coupled use of the precipitation anomaly percentage (Pa) index and the theory of runs. The Copula function was applied to establish the joint distribution model of characteristic variables, obtaining the drought frequency and drought return periods. Combined with the Jensen model, the agricultural drought loss rate under different drought return periods in the target year (2020) was calculated and evaluated. The results showed that the Gumbel-Hougaard copula function was suitable for the joint distribution of drought joint variables in Zunyi City. From 1956 to 2020, fewer droughts occurred in Zhengan and Wuchuan, and the most droughts took place in Fenggang, Meitan, and Yuqing. The average drought duration in each county was about 1.5 months, and the average drought severity was about 0.35 in spatial distribution. Crop loss rate caused by drought increased and the affected area expanded with the increase of drought return periods (5, 10, 20, 50, and 100 years) in temporal distribution. Meanwhile, the drought disaster was most drastic in the eastern region, followed by the south, north, west, and central area. The results were highly consistent with the historical drought in Zunyi City, which verified the validity of the model. This study could provide scientific knowledge for drought resistance and reasonable mitigation programing for the security of the regional agricultural production and the sustainability of social and economic development.

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Maximum Likelihood Estimation Methods for Copula Models

Cited by 9 publications

References 31 publications

A Multivariate Frequency Analysis Framework to Estimate the Return Period of Hurricane Events Using Event‐Based Copula

A Multivariate Frequency Analysis Framework to Estimate the Return Period of Hurricane Events Using Event‐Based Copula

Performance Degradation Modeling and Continuous Worktime Assessment of Ultrasonic Vibration Systems

A New Agricultural Drought Disaster Risk Assessment Framework: Coupled a Copula Function to Select Return Periods and the Jensen Model to Calculate Yield Loss

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