Quantile-based information generating functions and their properties and uses

Information generating functions (IGFs) have been of great interest to researchers due to their ability to generate various information measures. The IGF of an absolutely continuous random variable (see Golomb, S. (1966). The information generating function of a probability distribution. IEEE Transa...

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Bibliographic Details
Published in:Probability in the engineering and informational sciences Vol. 38; no. 4; pp. 733 - 751
Main Authors: Kayal, Suchandan, Balakrishnan, N.
Format: Journal Article
Language:English
Published: Cambridge Cambridge University Press 01.10.2024
Subjects:
Codes
Continuity (mathematics)
Density functions
Distribution functions
Entropy
Information theory
Lifetime
Quantiles
Random variables
ISSN:0269-9648, 1469-8951
Online Access:Get full text
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Summary:Information generating functions (IGFs) have been of great interest to researchers due to their ability to generate various information measures. The IGF of an absolutely continuous random variable (see Golomb, S. (1966). The information generating function of a probability distribution. IEEE Transactions in Information Theory , 12(1), 75–77) depends on its density function. But, there are several models with intractable cumulative distribution functions, but do have explicit quantile functions. For this reason, in this work, we propose quantile version of the IGF, and then explore some of its properties. Effect of increasing transformations on it is then studied. Bounds are also obtained. The proposed generating function is studied especially for escort and generalized escort distributions. Some connections between the quantile-based IGF (Q-IGF) order and well-known stochastic orders are established. Finally, the proposed Q-IGF is extended for residual and past lifetimes as well. Several examples are presented through out to illustrate the theoretical results established here. An inferential application of the proposed methodology is also discussed
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ISSN:0269-9648
1469-8951
DOI:10.1017/S0269964824000068