A New Information Theoretic Measure of PDF Symmetry

In this paper, a new quantity called symmetric information potential (SIP) is proposed to measure the reflection symmetry and to estimate the location parameter of probability density functions. SIP is defined as an inner product in the probability density function space and has a close relation to information theoretic learning. A simple nonparametric estimator directly from the data exists. Experiments demonstrate that this concept can be very useful dealing with impulsive data distributions, in particular, α-stable distributions.