Geometric Modeling in Probability and Statistics

Abstract

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Generalized Maxwell Relations in Thermodynamics with Metric Derivatives

“…Additionally, against the idea that entropy and disorder are always the same, see Reference [31]. In the sense of information theory, entropy is related to aspects and problems of information and communication [32]. In addition, in the context of information theory, the important concept of informational energy is that related to classical mechanics, and can be considered as a measure of the uncertainty or randomness of a probability system [32].…”

“…In the sense of information theory, entropy is related to aspects and problems of information and communication [32]. In addition, in the context of information theory, the important concept of informational energy is that related to classical mechanics, and can be considered as a measure of the uncertainty or randomness of a probability system [32]. Here, one adopts the conciliatory sense-namely, that entropy describes the amount of disorder or randomness in a system bearing energy or information [32], and that can be also used to evaluate aspects of uncertainty.…”

“…In addition, in the context of information theory, the important concept of informational energy is that related to classical mechanics, and can be considered as a measure of the uncertainty or randomness of a probability system [32]. Here, one adopts the conciliatory sense-namely, that entropy describes the amount of disorder or randomness in a system bearing energy or information [32], and that can be also used to evaluate aspects of uncertainty. In this broader sense, there are some generalized entropic forms which are particularly inspired in the context of information theory; for instance, Havdra-Charvat-Tsallis (HCT), Sharma-Mittal (SM), Sharma-Taneja (ST), and attempts to construct a generalized statistics with these forms.…”

Evaluating the risk of unsatisfied random demand on a time interval

“…The probability of exactly k random demands k ≤ r on the time interval (0, L) and no unsatisfied demand is given by (10) According to the total probability theorem, the probability that there will be no unsatisfied demand is given by (11) which results in (12) where r = [L/d] + 1.…”

“…[2][3][4][5][6] Neither of these classical comprehensive texts nor more recent comprehensive texts devoted to various problems in probability and queuing theory [7][8][9][10][11][12] treats the question related to risk of unsatisfied demand from random requests on a time interval.…”