SIMILARITY MEASURE FOR TWO DENSITIES

Document Type: Regular Paper

Authors

1 1Department of Statistics, College of Sciences, Shiraz University, 71454 Shiraz, I. R of Iran

2 Department of Mathematics, Shiraz Islamic Azad University, Shiraz, I. R of Iran

Abstract

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, θ1)f2(x, θ2)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 Scott's 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.

Keywords