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Automated detection of breast tumor in early stages using B-Mode Ultrasound image is crucial for preventing widespread breast cancer specially among women. This paper is primarily focusing on the classification of breast tumors through statistical modelling such as Rician inverse Gaussian (RiIG) pdf of contourlet transformed B-Mode image of breast tumors which is not reported yet in other earlier works. The suitability of RiIG distribution in modeling the contourlet coefficients is illustrated and compared with that of Nakagami distribution. The proposed method consists of pre-processing to remove the speckle noise, segmentation of the lesion region, contourlet transform on the B-Mode Ultrasound image and using the corresponding contourlet sub-band coefficients and the RiIG parameters, production of contourlet parametric (CP) images and weighted contourlet parametric (WCP) images. A number of geometrical, statistical, and texture features are calculated from B-Mode and the contourlet parametric images. In order to classify the features, seven different classifiers are employed. The proposed approach is applied to two different datasets (Mendeley Data and Dataset B) those are available publicly. It is shown that with parametric images, accuracies in the range of 94-97% are achieved for different classifiers. Specifically, with the support vector machine and k-nearest-neighbor classifier, very high accuracies of 97.2% and 97.55% can be obtained for the Mendeley Data and Dataset B,respectively, using the weighted contourlet parametric images.The reported classification performance is also compared with that of other works using the datasets employed in this paper. It is seen that the proposed approach using weighted contourlet parametric images can provide a superior performance.