Abstract
We consider a generalization of Awad–Shannon entropy, namely Awad–Varma entropy, introduce a stochastic order on Awad–Varma residual entropy and study some properties of this order, like closure, reversed closure and preservation in some stochastic models (the proportional hazard rate model, the proportional reversed hazard rate model, the proportional odds model and the record values model).
Highlights
The concept of entropy has its roots in Communication Theory and was introduced by Shannon
We consider a generalization of Awad–Shannon entropy, namely Awad–Varma entropy, introduce a stochastic order on Awad–Varma residual entropy and study some properties of this order, like closure, reversed closure and preservation in some stochastic models
For the remainder of the paper we present the preservation of the Awad–Varma quantile entropy order in the proportional hazard rate model, the proportional reversed hazard rate model, the proportional odds model and the record values model
Summary
The concept of entropy has its roots in Communication Theory and was introduced by Shannon. Shannon taked into account many methods to compress, encode and transmit messages from a data source and showed that the entropy is an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel He generalized and strengthened this result considerably for noisy channels in his noisy channel coding theorem. Working with other entropies, we can have completely different systems with the same entropy, the entropy is not necessarily nonnegative, the entropy of a continuous random variable is not a natural extension of the entropy of a discrete random variable, despite they have analogous form etc None of these situations occur in the case of Awad–Shannon entropy.
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