The paper deals with using so called singularity exponent in a classifier that is based on ordered distances of patterns to a given (classified) pattern. The approximation of probability distribution mapping function of the distribution of points from the viewpoint of distances from a given point in a form of a suitable power (exponent) of a distance is presented together with a way how to state it. A classifier utilizing knowledge about explored data distribution in a space and a suggested expression of the exponent is presented. Experimental results on both synthetic and real-life data show interesting behavior (classification accuracy) of the classifier in comparison with other well-known classifiers.