Pen based inputs are natural for human beings. A hand-drawn shape (symbol) can be used for various purposes, like, a command gesture, an input for authentication purpose, etc. Shape of a symbol is invariant to scale, translation, mirror-reflection and rotation of the symbol. Moments, like Zernike moments are often used to represent a symbol. Descriptors based on Zernike moments are rotation invariant, but since they are neither translation nor scale invariant, a normalization step as pre-processing is required. Apart from this, higher order Zernike moments are error prone. The present paper, proposes to use probability distributions of some local moments of lower order, as a representation scheme. Theoretically it is shown to possess all invariance properties. Experimentally, using the k-nearest neighbor classifier (with Kullback-Leibler distance), it is shown to perform better than Zernike moments based representation scheme. © 2011 Springer-Verlag.