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math.PR2024
Probabilistic Cauchy Functional Equations
Ehsan Azmoodeh, Noah Beelders, Yuliya Mishura
In this short note, we introduce probabilistic Cauchy functional equations, specifically, functional equations of the following form: $$ f(X_1 + X_2) \stackrel{d}{=} f(X_1) + f(X_2…
cs.IT2024
Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter
Volodymyr Braiman, Anatoliy Malyarenko, Yuliya Mishura +1
We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More prec…