In the following, it will be shown that the absolute minimum value of a given PMF isrelated to the limit of the Generalized Renyi entropy, as α → −∞ and β is fixed or (β → −∞ and α isfixed).The absolute maximum value of a PMF is related to the limit of the Generalized Renyi entropy, asα → ∞ and β is fixed or (β → ∞ and α is fixed).
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Alencar and Francisco (1998) proved the absolute minimum and maximum value of a given probabilitymass function is related to the limit of the Renyi entropy.In this paper, we have determined the minimum or maximum of some probability mass function (PMF)using this point.
📊
Key Findings & Data:Alencar and Francisco (1998) proved the absolute minimum and maximum value of a given probabilitymass function is related to the limit of the Renyi entropy.In this paper, we have determined the minimum or maximum of some probability mass function (PMF)using this point.
💡
Conclusion & Impact:In the following, it will be shown that the absolute minimum value of a given PMF isrelated to the limit of the Generalized Renyi entropy, as α → −∞ and β is fixed or (β → −∞ and α isfixed).The absolute maximum value of a PMF is related to the limit of the Generalized Renyi entropy, asα → ∞ and β is fixed or (β → ∞ and α is fixed).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Alencar and Francisco (1998) proved the absolute minimum and maximum value of a given probabilitymass function is related to the limit of the Renyi entropy.In this paper, we have determined the minimum or maximum of some probability mass function (PMF)using this point. In the following, it will be shown that the absolute minimum value of a given PMF isrelated to the limit of the Generalized Renyi entropy, as α → −∞ and β is fixed or (β → −∞ and α isfixed).The absolute maximum value of a PMF is related to the limit of the Generalized Renyi entropy, asα → ∞ and β is fixed or (β → ∞ and α is fixed).
🔖
Cite This Article
Borzadaran, G. R. M., TABASS, M. S. (2022). Absolute Minimum and Maximum of the Probability Mass Functions and Limit of Generalized Renyi Entropy. Mathematical Sciences and Applications E-Notes, Cilt: 7 - Sayı: 1, 113–119. https://ajindex.com/articles/578857
Alencar, M.S. and Francisco, M.A., The absolute minimum and maximum value problem and the Renyi entropy of order α. Telecommunications Symposium, 1(1998), 239-241
Hartley, R.V.L., Transmission of information. Bell System Tech. J., (1928), 7, 535-563
Inusah. S. and Kozubowski, T.J., A discrete analogue of the Laplace distribution. Journal of statistical planning and inference, (2006), 136, 1090-1102
Koski, T. and Persson, L,E., Some properties of generalized exponential entropies with applications to data compression. Information Sciences, (1992), 62, 103-132
Kozubowski, T.J. and Inusah, S., A skew Laplace distribution on integers. The Institute of Statistical Mathematics, (2006), 58, 555-571
Renyi, A., On measures of entropy and information. Proc. Berekeley Symposium, Statist. Probability, 1961, 1, 547-561
Shannon, C.E., A Mathimatical Theory of Communication. Bell System Tech., (1948), 27, 379-423.