Maximum Certainty Principle. Theoretical Analysis of a New Probabilistic Invariant with Applications in the Quito-Ecuador Storm Study

Abstract

A new probabilistic invariant named Maximum Certainty (N_max) is exposed finding the extremum of the Functional Certainty (N) with variational calculus, equivalent to the principle developed by Euler-Lagrange in the deterministic field known as Least Action. Its emergence comes naturally when regard the conservation of the Information received and delivered by a probabilistic system. The invariant N_max associated to a random variable T, balances the Knowledge function C(t); of each probabilistic density function f(t)_max, and Information function: I(t)=-ln(f(t)_max). It starts by proving N_max for the truncated exponential cumulative distribution function and is extended as a principle to other probability distribution families, both continuous and discrete both bounded and unbounded. When the random variable T has units of time, truncated in DT, the cumulative distribution function P(t)_max obtained is the most probable time curve among all the possible ones. The modeling of stochastic storm patterns in Quito-Ecuador through the Truncated Quadratic Exponential Distribution (with parameter alfa=9.8) is given as an example of application, among others.