A measure of mutual complete dependence in discrete variables through subcopula

Shan, Qingsong; Wongyang, Tanes; Wang, Tonghui; Tasena, Santi

doi:10.1016/j.ijar.2015.04.005

Cited by 15 publications

(4 citation statements)

References 11 publications

(15 reference statements)

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“…Six clustering indicators, namely mean, standard deviation, number of peaks and valleys, coefficient of variation, kurtosis and skewness, are selected as the clustering features [27]. The historical power output is statistically analysed via feature clustering.…”

Section: Influencing Factors Of Pv Generationmentioning

confidence: 99%

Robust optimisation of electricity‐heating integrated energy system based on data‐driven PV interval estimation

Xu,

Liu,

Guo

et al. 2023

IET Energy Syst Integration

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Short‐term interval estimation can effectively and precisely quantify the uncertainties of renewable energy, accurately represent the range of fluctuations of uncertain variables in robust optimisation of electricity‐heating integrated energy system (EHIES) and it is getting crucial for reliable and flexible operation of renewable dominated new energy systems. The authors present a multivariate data‐driven short‐term PV power interval prediction model that consists of multiple layers, including one‐dimensional convolutional layer, ultra‐lightweight subspace attention mechanism (ULSAM), bidirectional long and short‐term memory (BiLSTM), quantile regression (QR) and kernel density estimation (KDE). The one‐dimensional convolutional layer and ULSAM can extract sequential features and highlight key information from the data; the BiLSTM processes time series data in both directions and conveys historical information; the QR and KDE models generate interval prediction with a given confidence level. Based on the proposed interval estimation, a refined PV uncertainty set can be established and adopted by robust optimal scheduling of EHIES utilising min‐max‐min algorithm. The simulation results have demonstrated the estimation accuracy and adaptability to various weather scenarios.

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Section: Influencing Factors Of Pv Generationmentioning

confidence: 99%

Robust optimisation of electricity‐heating integrated energy system based on data‐driven PV interval estimation

Xu,

Liu,

Guo

et al. 2023

IET Energy Syst Integration

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“…The concept of copula originated from Sklar's theorem. A copula joins univariate distribution functions of random variables to form multivariate (joint) distribution functions to describe the dependence structure among variables [34,35]. Kreinovich et al [36] mentioned that the copula is the most efficient way of representing multidimensional distributions and, thus, has been successfully applied to many applications in statistics.…”

Section: Copula Functionsmentioning

confidence: 99%

“…Thus, it is crucial to allow the total cost (Equation (32)) and output price (Equation (33)) to be correlated. In the simultaneous SFM with dependent error components, the dependence between the error components w 1it and v 1it , and w 2it and v 2it were modelled by copulas, as shown in Equations (34) and (35). Moreover, the composed error terms ε 1it and ε 2it were also permitted to be dependent, following Equation (36).…”

Section: Model and Datamentioning

confidence: 99%

A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry

Liu

Rahman

et al. 2020

Mathematics

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The paper develops a simultaneous equations stochastic frontier model (SFM) with dependent random noise and inefficiency components of individual equations as well as allowing dependence across all equations of the model using copula functions. First, feasibility of our developed model was verified via two simulation studies. Then the model was applied to assess cost efficiency and market power of the banking industry of China using a panel data of 37 banks covering the period 2013–2018. Results confirmed that our simultaneous SFM with dependent random noise and inefficiency components outperformed its predecessor, which is a simultaneous SFM with dependent composite errors but with independent random noise and inefficiency components of individual SFMs as well as the conventional single-equation SFM. Apart from the statistical and computational superiority of our developed model, we also see that Chinese banks in general have a high level of cost efficiency and that competition in the banking industry of China mainly exists in state-owned banks and joint stock banks. Presence of economies of scales as well as diseconomies of scales were found in different banks. Also, the state-owned banks embraced most sophisticated technologies thereby allowing them to operate with the highest level of cost efficiency.

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“…Every complete dependence copula can be written in the form C e,f or C f,e for some measure-preserving transformation f [9,21]. Despite its simplistic and deterministic nature, complete dependence copulas are ubiquitous and useful in theoretical studies of copulas [19,20,21].…”

Section: Introductionmentioning

confidence: 99%

Generalized factorizability of certain implicit dependence copulas

Panyasakulwong¹

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The copula CX,Y of random variables X and Y that are uniformly distributed on [0,1] is called an implicit dependence copula if f(X)=g(Y) almost surely for some Borel functions f and g on [0,1]. Via a generalized Markov product, we give a one-to-one correspondence between the implicit dependence copulas and the parametric classes of subcopulas on a corresponding domain for the cases that f=g=Λθ, the tent function whose top is at (θ,1). We also show in the case f=g=α, a simple measure-preserving function, that implicit dependence copulas are generalized factorizable.

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A measure of mutual complete dependence in discrete variables through subcopula

Cited by 15 publications

References 11 publications

Robust optimisation of electricity‐heating integrated energy system based on data‐driven PV interval estimation

Robust optimisation of electricity‐heating integrated energy system based on data‐driven PV interval estimation

A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry

Generalized factorizability of certain implicit dependence copulas

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