SIMILARITY MEASURE FOR TWO DENSITIES

Scott and Szewczyk in Technometrics, 2001, have introduced a similarity measure for two densities f1 and f2 , by 1, 2 1 2 1 1 2 2 ( , ) , , f f sim f f f f f f < > = < > < > where f1, f2 f1(x, ?1)f2(x, ?2)dx. +? ?? < > =? sim(f1, f2) has some appropriate properties that can be suitable measures for the similarity of f1 and f2 . However, due to some restrictions on the value of parameters and the kind of densities, discrete or continuous, it cannot be used in general. The purpose of this article is to give some other measures, based on modified Scottʹs measure, and Kullback information, which may be better than sim(f1, f2) in some cases. The properties of these new measures are studied and some examples are provided.