A New Weighted Information Generating Function for Discrete Probability Distributions

TL;DR

This paper introduces a new weighted information generating function for discrete probability distributions, linking its derivative at 1 to known information measures, and explores its properties and special cases.

Contribution

It proposes a novel weighted information generating function and analyzes its properties, expanding the tools for measuring information in discrete distributions.

Findings

Derivative at 1 relates to known information measures

Properties of the new generating function are characterized

Special cases of the function are identified

Abstract

The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have also been studied.