Buruli ulcer and tuberculoid leprosy are two skin diseases affecting virtually the same areas of the body. In the early state on black skin, the skin affected by these diseases has not only few specificities but especially a low contrast with healthy skin. Which makes any diagnosis difficult. However, these diseases, which are belatedly detected or badly treated, cause aesthetic bodily damage and also major handicaps. The present work therefore focuses on this early diagnosis and is based on the characterization of the textures of these affections in the macroscopic images of the black skin. For this purpose, a baseline of these two diseases certified by dermatologists is set up. Then with MATLAB R2015a, we extract the textures in the digital images of the certified affections and the affection to be identified by the Haar wavelet transform. The histograms of the obtained detail images are approximated by a family of non-zero mean Asymmetric Gaussian Distributions (AGGD). The Gaussian distribution that best fits the histogram for each image is determined after the Kolmogorov-Smirnov fit test. The parameters of this Gaussian Distribution are the characteristics of the textures for each condition. Finally, based on these characteristics, the Jeffreys divergence is calculated and allows to identify Buruli ulcer and tuberculoid leprosy. Applied to multiple disease images, the non-zero mean AGGD model provided an identification rate of 90% versus 66.66% for the existing zero average AGGD model.