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Table Of Integrals Series And Products

생체의 모델링과 Simulation

This programming manual accompanies the PcGive Professional 9.0 software, an interactive modelling package for modelling statistical and economic data for forecasting or observing trends.

Object-orientd matrix programming using OX

Review: Divergence measures for statistical data processing-An annotated bibliography

Wiley Series in Pure and Applied Optics

Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser, and synthetic aperture radar, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G 0 distribution and, under which, regions with different degrees of roughness and mean brightness can be characterized by two parameters; a third parameter, which is the number of looks, is related to the overall signal-to-noise ratio. Assessing distances between samples is an important step in image analysis; they provide grounds of the separability and, therefore, of the performance of classification procedures. This paper derives and compares eight stochastic distances and assesses the performance of hypothesis tests that employ them and maximum likelihood estimation. We conclude that tests based on the triangular distance have the closest empirical size to the theoretical one, while those based on the arithmetic-geometric distances have the best power. Since the power of tests based on the triangular distance is close to optimum, we conclude that the safest choice is using this distance for hypothesis testing, even when compared with classical distances as Kullback-Leibler and Bhattacharyya.

Hypothesis Testing in Speckled Data With Stochastic Distances

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric synthetic aperture radar data whose adequacy is attested in this paper. Classification, segmentation, and image analysis techniques that depend on this model are devised, and many of them employ some type of dissimilarity measure. In this paper, we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained that lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.

We study a new family of continuous distributions with two extra shape parameters called the Burr generalized family of distributions. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for some of its mathematical quantities. The estimation of the model parameters is performed by maximum likelihood. We prove the flexibility of the new family by means of applications to two real data sets. Furthermore, we propose a new extended regression model based on the logarithm of the Burr generalized distribution. This model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.

Odd-Burr generalized family of distributions with some applications

Polarimetric synthetic aperture radar (PolSAR) has achieved a prominent position as a remote imaging method. However, PolSAR images are contaminated by speckle noise due to the coherent illumination employed during the data acquisition. This noise provides a granular aspect to the image, making its processing and analysis (such as in edge detection) hard tasks. This paper discusses seven methods for edge detection in multilook PolSAR images. In all methods, the basic idea consists in detecting transition points in the finest possible strip of data which spans two regions. The edge is contoured using the transitions points and a B-spline curve. Four stochastic distances, two differences of entropies, and the maximum likelihood criterion were used under the scaled complex Wishart distribution; the first six stem from the h-φ class of measures. The performance of the discussed detection methods was quantified and analyzed by the computational time and probability of correct edge detection, with respect to the number of looks, the backscatter matrix as a whole, the SPAN, the covariance an the spatial resolution. The detection procedures were applied to three real PolSAR images. Results provide evidence that the methods based on the Bhattacharyya distance and the difference of Shannon entropies outperform the other techniques.

Abraão D. C. Nascimento

Papers

Hypothesis Testing in Speckled Data With Stochastic Distances

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

Odd-Burr generalized family of distributions with some applications

Comparing Edge Detection Methods Based on Stochastic Entropies and Distances for PolSAR Imagery