Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior

2024/11/25 by Dmitri Finkelshtein, Finkelshtein, Dmitri, Anatoliy Malyarenko +5
Engineering · #94A17 #Elasticity and Wave Propagation #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2411.16913

openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper extends the analysis of the entropies of the Poisson distribution with parameter λ. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to λ, whereas two generalized forms of the Rényi entropy may exhibit "anomalous" (non-monotonic) behavior. Additionally, we examine the asymptotic behavior of the entropies as λ→ ∞ and provide both lower and upper bounds for them.

Related

• Properties of Shannon and Rényi entropies of the Poisson distribution as the functions of intensity parameter
• Properties of the Shannon, Rényi and other entropies: dependence in parameters, robustness in distributions and extremes
• Bounds for some entropies and special functions
• Complete monotonicity of some entropies
• Inequalities for indices of coincidence and entropies