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Journal of Probability and Statistics
Volume 2013, Article ID 170967, 13 pages
Research Article

Masses of Negative Multinomial Distributions: Application to Polarimetric Image Processing

1Université de Pau et des Pays de l'Adour, Avenue de l'Université, 64012 Pau, France
2Gipsa-Lab, Département Images et Signal, 961 rue de la Houille Blanche, BP 46, 38402 Saint Martin d'Héres, France
3Université de Toulouse, IRIT/ENSEEIHT/TESA, 2 rue Charles Camichel, BP 7122, 31071 Toulouse Cedex 7, France

Received 5 June 2012; Revised 30 October 2012; Accepted 8 November 2012

Academic Editor: Edwin Ortega

Copyright © 2013 Philippe Bernardoff et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper derives new closed-form expressions for the masses of negative multinomial distributions. These masses can be maximized to determine the maximum likelihood estimator of its unknown parameters. An application to polarimetric image processing is investigated. We study the maximum likelihood estimators of the polarization degree of polarimetric images using different combinations of images.