Information is Key: Parametric Information Theory, The Signal-to-Noise Paradigm, Stochastic Distributions and Logarithmic Functions

Every student of probability knows that E(X+Y) = E(X) + E(Y). In words, given two random variables, the expected value of their sum is the sum of their expected values.Based on the logarithm, this book introduces the fundamental concept of expected information L(X), which has the remarkable property L(XY) = L(X) + L(Y).Consistently, the corresponding theory is developed, which tackleshigher logarithmic moments of random variables & their distributions, and the `information variance' in particular,modified information parameters and associated logarithmic functions,the discrete and the multidimensional cases,general patterns --- most notably the algebra of random variables, and the stochastic Askey scheme, i.e., a logical map of all distributions,the Signal-to-Noise paradigm.Since the book extends basic stochastic ideas and touches upon combinatorics and special functions, it should be of interest to all those dealing with probability and its ilk - most statisticians, many mathematicians, quite a few scientists, and some philosophers.The book of nature is written in the language of mathematics, and information ranks among its key concepts. Read more