Description
Multifunction copula generator.
Use Cases
Quantitative finance
In quantitative finance copulas are applied to risk management, to portfolio management and optimization, and to derivatives pricing.
Copulas aid in analyzing the effects of downside regimes by allowing the modelling of the marginals and dependence structure of a multivariate probability model separately.
Quantum Random Numbers for Security and Cryptography
Random numbers are important in computing. TCP/IP sequence numbers, TLS nonces, ASLR offsets, password salts, and DNS source port numbers all rely on random numbers. In cryptography randomness is found everywhere, from the generation of keys to encryption systems.
Some applications where the QRNG can be applied are:
- Secure wireless communications, including 802.11i, 802.15.3, 802.15.4 (ZigBee), MBOA, 802.16e
- Electronic financial transactions
- Content protection, digital rights management (DRM), set-top boxes
- Secure RFID
- Secure Smart Cards
Civil engineering
Copula functions have been successfully applied to the database formulation for the reliability analysis of highway bridges, and to various multivariate simulation studies in civil engineering, reliability of wind and earthquake engineering,[40] and mechanical & offshore engineering.
Reliability engineering
Copulas are being used for reliability analysis of complex systems of machine components with competing failure modes.
Warranty data analysis
Copulas are being used for warranty data analysis in which the tail dependence is analysed.
Turbulent combustion
Copulas are used in modelling turbulent partially premixed combustion, which is common in practical combustors.
Medicine
Copulas have many applications in the area of medicine:
- Used in the field of magnetic resonance imaging (MRI), for example, to segment images, to fill a vacancy of graphical models in imaging genetics in a study on schizophrenia, and to distinguish between normal and Alzheimer patients.
- Used in the area of brain research based on EEG signals, for example, to detect drowsiness during daytime nap, to track changes in instantaneous equivalent bandwidths (IEBWs), to derive synchrony for early diagnosis of Alzheimer’s disease, to characterize dependence in oscillatory activity between EEG channels, and to assess the reliability of using methods to capture dependence between pairs of EEG channels using their time-varying envelopes.
- A copula model has been developed in the field of oncology, for example, to jointly model genotypes, phenotypes, and pathways to reconstruct a cellular network to identify interactions between specific phenotype and multiple molecular features (e.g. mutations and gene expression change).
Geodesy
The combination of SSA and Copula-based methods have been applied for the first time as a novel stochastic tool for EOP prediction.
Hydrology research
Copulas have been used in both theoretical and applied analyses of hydroclimatic data. Theoretical studies adopted the copula-based methodology for instance to gain a better understanding of the dependence structures of temperature and precipitation, in different parts of the world. Applied studies adopted the copula-based methodology to examine e.g., agricultural droughts or joint effects of temperature and precipitation extremes on vegetation growth.
Climate and weather research
Copulas have been extensively used in climate- and weather-related research.
Solar irradiance variability
Copulas have been used to estimate the solar irradiance variability in spatial networks and temporally for single locations.
Random vector generation
Large synthetic traces of vectors and stationary time series can be generated using empirical copula while preserving the entire dependence structure of small datasets; such empirical traces are useful in various simulation-based performance studies.
Ranking of electrical motors
Copulas have been used for quality ranking in the manufacturing of electronically commutated motors.
Signal processing
Copulas are important because they represent a dependence structure without using marginal distributions. Copulas have been widely used in the field of finance, but their use in signal processing is relatively new. Copulas have been employed in the field of wireless communication for classifying radar signals, change detection in remote sensing applications, and EEG signal processing in medicine. In this section, a short mathematical derivation to obtain copula density function followed by a table providing a list of copula density functions with the relevant signal processing applications are presented.
