Abstract
Recently, a series of divergence measures have emerged from information theory and statistics and numerous inequalities have been established among them. However, none of them are a metric in topology. In this paper, we propose a class of metric divergence measures, namely, , and study their mathematical properties. We then study an important divergence measure widely used in credit scoring, called information value. In particular, we explore the mathematical reasoning of weight of evidence and suggest a better alternative to weight of evidence. Finally, we propose using as alternatives to information value to overcome its disadvantages.
Highlights
We propose a class of metric divergence measures, namely, Lp(P ‖ Q), P ≥ 1, and study their mathematical properties
We study an important divergence measure widely used in credit scoring, called information value
The information measure is an important concept in Information theory and statistics
Summary
The information measure is an important concept in Information theory and statistics. For all P, Q ∈ Δ n, the following divergence measures are well known in the literature of information theory and statistics. Cressie and Read [13] considered the one-parametric generalization of information measure D(P ‖ Q), called the relative information of type s given by n Taneja proved [14] that all the 3 s-type information measures Ds(P ‖ Q), Vs(P ‖ Q), and Ws(P ‖ Q) are nonnegative and convex in the pair (P, Q). He obtained inequalities regarding the various divergence measures:.
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