scholarly journals A Procustes's Procedure for Obtaining Divergences

2021 ◽  
Author(s):  
Leonardo Riveaud ◽  
Mateos Diego ◽  
Pedro Walter Lamberti
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Real Time ◽  
Probability Distributions ◽  
Convexity Property ◽  
Weighted Probability ◽  
Kernel Theory

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application a more appropriate measure may be necessary. In this paper we introduce a family of divergences we call gamma-divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series.

scholarly journals Gamma-Divergence. An Introduction to New Divergence Family

2020 ◽  
Author(s):  
Leonardo Riveaud ◽  
Mateos Diego ◽  
Pedro Walter Lamberti
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Real Time ◽  
Probability Distributions ◽  
Convexity Property ◽  
Weighted Probability

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application, a more appropriate measure may be necessary. In this paper we introduce a family of divergences called γ-Divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. In addition, we define a generalised entropy closely related to the γ-Divergences. Finally, we apply our findings to the analysis of simulated and real time series.

Parameterization of multifractal cascade models based on their breakdown coefficients

2020 ◽  
Author(s):  
César Aguilar Flores ◽  
Alin Andrei Carsteanu
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Rainfall Intensity ◽  
Probability Distributions ◽  
Asymptotic Properties ◽  
Distribution Functions ◽  
Marginal Probability ◽  
Probability Distribution Functions ◽  
Marginal Probability Distribution ◽  
Cascade Models

<p>Breakdown coefficients of multifractal cascades have been shown, in various contexts, to be ergodic in their (marginal) probability distribution functions, however the necessary connection between the cascading process (or a tracer thereof, such as rainfall) and the breakdown coefficients of the measure generated by the cascade, was missing. This work presents a method of parameterization of certain types of multiplicative cascades, using the breakdown coefficients of the measures they generate. The method is based on asymptotic properties of the probability distributions of the breakdown coefficients in “dressed” cascades, as compared with the respective distributions of the cascading weights. An application to rainfall intensity time series is presented.</p>

scholarly journals SINGLE AND MULTI-SITE OPERATIONAL HYDROLOGY

1972 ◽  
Vol 3 (4) ◽  
pp. 214-238 ◽  
Author(s):  
T. A. McMAHON ◽  
G. P. CODNER ◽  
C. PHILIPS
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Historical Data ◽  
Probability Distributions ◽  
Supply System ◽  
Random Component ◽  
Historical Time ◽  
Site Analysis ◽  
Normal Transformation ◽  
Log Normal

This paper reviews several different single- and multi-site generation models to complement those papers in which the models are developed but not applied. Initially the historical time series is looked at using various time series techniques, including correlograms and spectral analyses, to determine whether a lag one Markov model will satisfactorily represent the historical data. The single site models which are examined include an empirical model using the historical probability distribution of the random component, the Thomas and Fiering model using both logarithms of the data and Matalas' log-normal transformation equations, and finally Moran's Gamma distribution. Matalas' Residual method with several probability distributions and Moran's Multivariate Gamma technique are used in the multi-site analysis. All models are applied to the streams of the Melbourne metropolitan water supply system.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

Research on the Distributed Characteristics of the Delay for Network Coding Based Real-Time Multicast in MANETs

2014 ◽  
Vol 530-531 ◽  
pp. 768-772
Author(s):  
Guo Ping Tan ◽  
Lin Feng Tan ◽  
Lei Cao ◽  
Mei Yan Ju
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Network Coding ◽  
Real Time ◽  
Lognormal Distribution ◽  
Ad Hoc ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Actual Distribution ◽  
Delay Distribution

For the study of the applications of partial network coding based real-time multicast protocol (PNCRM) in Mobile Ad hoc networks, the researches should be developed in the probability distribution of delay. In this paper, NS2 is used to obtain the delay of data packets through simulations. Because the delay does not obey the strict normal distribution, the maximum likelihood estimate method based on the lognormal distribution is used to process the data. Using MATLAB to obtain the actual distribution of the natural logarithm of delay, then drawing the delay distribution with the maximum likelihood estimation method based on the lognormal distribution, the conclusion that the distributions obtained by the above mentioned methods are basically consistent can be obtained. So the delay distribution of PNCRM meets the lognormal distribution and the characteristic of delay probability distribution can be estimated.

A Reliability-Based Early Warning System for Real-Time Monitoring on RC Buildings

2012 ◽  
Vol 446-449 ◽  
pp. 3422-3427
Author(s):  
Wang Sheng Liu ◽  
Ming Zhao
Keyword(s):  
Probability Distribution ◽  
Real Time ◽  
Early Warning ◽  
Early Warning System ◽  
Limit State ◽  
Warning System ◽  
State Function ◽  
Real Time Monitoring ◽  
Rc Buildings ◽  
Load Effect

Today there is an urgent need for effective monitoring whether for old buildings or new ones. While conventional early warning system for real-time monitoring is based on safety factor, this paper proposes a new reliability-based framework to monitor the safety of RC buildings probabilistically. The framework includes modeling resistance, predicting probability distribution of load effect, calculating reliability and setting reliability index threshold. The in-situ test data enables to update the resistance model through a Bayesian process. Meanwhile, the observed monitoring data predicts the probability distribution of load effect. FORM is used to calculate the reliability because the limit state function for real-time monitoring is linear and simple. This study shows that the reliability-based early warning system is of more scientific sense in quantifying the safety and may be applied to many engineering fields.

Sign in / Sign up

Export Citation Format

Share Document