scholarly journals Characterization of probability distribution convergence in Wasserstein distance by $L^{p}$-quantization error function

Bernoulli ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 1171-1204
Author(s):  
Yating Liu ◽  
Gilles Pagès
Keyword(s):  
Probability Distribution ◽  
Error Function ◽  
Wasserstein Distance ◽  
Quantization Error

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

scholarly journals Probability Forecast Combination via Entropy Regularized Wasserstein Distance

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 929
Author(s):  
Ryan Cumings-Menon ◽  
Minchul Shin
Keyword(s):  
Wasserstein Distance ◽  
Tuning Parameter ◽  
Forecast Combination ◽  
Probability Forecast ◽  
Density Forecast ◽  
Combination Methods ◽  
Multivariate Gaussian ◽  
Density Forecasting ◽  
Gaussian Input

We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the assumption. More specifically, we show that the regularized Wasserstein barycenter between multivariate Gaussian input densities is multivariate Gaussian, and provide a simple way to compute mean and its variance–covariance matrix. Second, we show how this type of regularization can improve the predictive power of the resulting combined density. Third, we provide a method for choosing the tuning parameter that governs the strength of regularization. Lastly, we apply our proposed method to the U.S. inflation rate density forecasting, and illustrate how the entropy regularization can improve the quality of predictive density relative to its unregularized counterpart.

A characterization of the exponential distribution

1972 ◽  
Vol 9 (02) ◽  
pp. 457-461 ◽  
Author(s):  
M. Ahsanullah ◽  
M. Rahman
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Lebesgue Measure ◽  
Random Variable ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positive Random Variable ◽  
Absolutely Continuous ◽  
Necessary And Sufficient

A necessary and sufficient condition based on order statistics that a positive random variable having an absolutely continuous probability distribution (with respect to Lebesgue measure) will be exponential is given.

Multi-Phase Texture Segmentation Using Gabor Features Histograms Based on Wasserstein Distance

2014 ◽  
Vol 15 (5) ◽  
pp. 1480-1500 ◽  
Author(s):  
Motong Qiao ◽  
Wei Wang ◽  
Michael Ng
Keyword(s):  
Gabor Filter ◽  
Error Function ◽  
Feature Space ◽  
Wasserstein Distance ◽  
Energy Functional ◽  
Phase Image ◽  
Minimization Method ◽  
Closed Form Solutions ◽  
Gabor Feature ◽  
Multi Phase

AbstractWe present a multi-phase image segmentation method based on the histogram of the Gabor feature space, which consists of a set of Gabor-filter responses with various orientations, scales and frequencies. Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function, which is a metric to measure the distance of two histograms. The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2. We test our model on both simple synthetic texture images and complex natural images with two or more phases. Experimental results are shown and compared to other recent results.

Identifying Elastic Properties of Isotropic Materials by Finite Element Analyses and Vibration Data

2007 ◽  
Vol 345-346 ◽  
pp. 1327-1330 ◽  
Author(s):  
Marco Alfano ◽  
Leonardo Pagnotta ◽  
Giambattista Stigliano
Keyword(s):  
Finite Element ◽  
Error Function ◽  
Finite Element Analyses ◽  
Vibration Testing ◽  
Isotropic Materials ◽  
Vibration Data ◽  
The Difference ◽  
Optimizing Algorithm ◽  
Non Destructive

The use of non destructive techniques for the elastic characterization of isotropic materials is continuously increasing and those based on the modal vibration testing of plate-like specimens is very widespread. In the present paper, an optimized search procedure is proposed which allows the material constants of isotropic plates to be non-destructively identified from vibration testing data and using finite element analyses. The identification process is performed by an optimizing algorithm in which the error function to be minimized depends on the difference between the natural frequencies obtained by finite element analyses and the measured ones. In order to verify the proposed identification procedure a comparison with the results reported in literature has been made.

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