copula density
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2021 ◽  
Anning Hu ◽  
Zhipeng Zhou

The sociological analysis of the mobility tables enhances the examination of the circulation mobility and helps one reveal the nuanced morphological patterns of mobility. In contrast, the economic analysis based on the measure of elasticity provides a handy way of covariate conditioning and statistically testing the similarities of mobility patterns across groups. In this article, we argue that the distinct methodological merits of these two approaches can be equipped by adopting a more comprehensive analytical framework using the copula functions: (1) The copula functions concern the dependence structure that is independent from the margins, which enable scholars to focus on the relative mobility; (2) The copula density, estimated either parametrically or non-parametrically, reveals the nuanced morphological mobility patterns; (3) By residualizing the marginal variables, the detected mobility pattern can be interpreted in a stronger causal sense; and (4) the Cramér–von Mises Test offers an easy-to-use statistic to conduct intergroup comparison of mobility patterns. The copula-based framework is illustrated by investigating the income mobility between 1978 and 2017 in the U.S., using the National Longitudinal Survey of Youth 1979 (NLSY79).

2020 ◽  
Vol 8 (4) ◽  
pp. 834-845
Morteza Mohammadi ◽  
Mohammad Amini ◽  
Mahdi Emadi

The purpose of this paper is to introduce two semiparametric methods for the estimation of copula parameter. These methods are based on minimum Alpha-Divergence between a non-parametric estimation of copula density using local likelihood probit transformation method and a true copula density function. A Monte Carlo study is performed to measure the performance of these methods based on Hellinger distance and Neyman divergence as special cases of Alpha-Divergence. Simulation results are compared to the Maximum Pseudo-Likelihood (MPL) estimation as a conventional estimation method in well-known bivariate copula models. These results show that the proposed method based on Minimum Pseudo Hellinger Distance estimation has a good performance in small sample size and weak dependency situations. The parameter estimation methods are applied to a real data set in Hydrology.

2020 ◽  
Faizan Anwar ◽  
András Bárdossy

<p>Phase randomization and its variants such as the Amplitude-adjusted (AAFT) and the Iterative amplitude adjusted (IAAFT) Fourier transform are used to check statistical significance of a given hypothesis and/or to generate time series that are similar to a reference in some statistical sense. These methods have the drawback of producing incorrect dependence structures e.g. empirical copula density, asymmetries and entropies. Recently, another form of such methods, “Phase Annealing”, was introduced, giving a possibility to generate n-dimensional realizations of a process under given constraint(s). The main concern using this method is the selection of correct objective function(s).</p><p>Here we show discharge time series generation using Phase Annealing with new objective functions. This allowed us to generate time series that are much longer than the reference, which in turn was helpful in establishing better distributions of floods.</p><p>We also show the generation of discharge time series at multiple locations that have the correct spatio-temporal dependences among all the series. Using the results, we generated full distributions of simultaneous extremes at observation locations.</p><p>Further uses may include clustering catchments that are likely to bring floods together and reliability analysis i.e. simulating distributions of failures for a system with many dependent/independent components. Drawbacks using this method are also shown.</p>

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1103 ◽  
Bajic ◽  
Skoric ◽  
Milutinovic-Smiljanic ◽  

This paper proposes a method that maps the coupling strength of an arbitrary number of signals D, D ≥ 2, into a single time series. It is motivated by the inability of multiscale entropy to jointly analyze more than two signals. The coupling strength is determined using the copula density defined over a [0 1]D copula domain. The copula domain is decomposed into the Voronoi regions, with volumes inversely proportional to the dependency level (coupling strength) of the observed joint signals. A stream of dependency levels, ordered in time, creates a new time series that shows the fluctuation of the signals’ coupling strength along the time axis. The composite multiscale entropy (CMSE) is then applied to three signals, systolic blood pressure (SBP), pulse interval (PI), and body temperature (tB), simultaneously recorded from rats exposed to different ambient temperatures (tA). The obtained results are consistent with the results from the classical studies, and the method itself offers more levels of freedom than the classical analysis.

Marko Mozetić ◽  
Tamara Škorić ◽  
Jelena Antelj ◽  
Katarina Otašević ◽  
Branislav Milovanović ◽  

Portapres® is a unique device that reliably accomplishes a challenging task of continuous and non-invasive recording ofblood pressure (BP) waveforms in moving subjects. The complex procedure of Portapres® signal acquisition includes periodic changesof cuffed fingers to avoid pain and stress, as well as the blood pressure correction due to the increasing and decreasing elevation of armposture. Due to these procedures, the recorded waveforms are corrupted. The aim of this paper is to analyze the influence of inevitableartifacts on parameters obtained from the blood pressure waveforms. The analyzed waveforms are obtained from healthy volunteers atBezanija Kosa Hospital, Belgrade. The parameters include systolic blood pressure (SBP) and pulse interval (PI) extracted byBeatscope® software. The interrelationship of SBP and PI signals forms a major cardiovascular feedback – baroreflex. It can beanalyzed using the sequence method for spontaneous baroreflex sensitivity, but the tools that reveal more profound dependencystructures include cross-approximate and cross-sample entropy, as well as the copula structures. The influence of artifacts, inevitable inPortapres® signals, is the main goal of this study. The analyses revealed that automatic artifact correction induced no significantchanges considering the statistical moments and the baroreflex sensitivity; the same applies to the copula density and rank tests. Theentropy analysis, however, turned out to be extremely sensitive so its implementation in Portapres® signal analysis is not recommended.

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