Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in multidimensions. We show that for a family of spherically symmetric distributions, these statistics have a Gumbel-type limit, generalizing several existing results. We also discuss the other two types of limit laws and suggest some open problems. This work complements our earlier study on the minimum interpoint distance.Comment: Published at http://dx.doi.org/10.1214/14-AAP1082 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The use of Mean Residual Life in testing departures from Esxponentiality.

vita media residua; test di esponenzialità; processo di wiener; processo di quantili

An Improved Approach for Contrast Enhancement of Spinal Cord Images based on Multiscale Retinex Algorithm

This paper presents a new approach for contrast enhancement of spinal cord medical images based on multirate scheme incorporated into multiscale retinex algorithm. The proposed work here uses HSV color space, since HSV color space separates color details from intensity. The enhancement of medical image is achieved by down sampling the original image into five versions, namely, tiny, small, medium, fine, and normal scale. This is due to the fact that the each versions of the image when independently enhanced and reconstructed results in enormous improvement in the visual quality. Further, the contrast stretching and MultiScale Retinex (MSR) techniques are exploited in order to enhance each of the scaled version of the image. Finally, the enhanced image is obtained by combining each of these scales in an efficient way to obtain the composite enhanced image. The efficiency of the proposed algorithm is validated by using a wavelet energy metric in the wavelet domain. Reconstructed image using proposed method highlights the details (edges and tissues), reduces image noise (Gaussian and Speckle) and improves the overall contrast. The proposed algorithm also enhances sharp edges of the tissue surrounding the spinal cord regions which is useful for diagnosis of spinal cord lesions. Elaborated experiments are conducted on several medical images and results presented show that the enhanced medical pictures are of good quality and is found to be better compared with other researcher methods.Comment: 13 pages, 6 figures, International Journal of Imaging and Robotics. arXiv admin note: text overlap with arXiv:1406.571