Estimation of the parameters of the particular solution of a partial differential equation through Cramer Rao

Abstract

The parameter estimation task is given by statistical exploration of probability density functions. The volume of samples and characteristics of a database is an advantage to solve the problem of parameter estimation but finding a function that models the behavior of a database or its distribution is complex and without this step it is not possible to use advanced statistical techniques. This document solves the problem of parameter estimation of a particular solution of a partial differential diffusion equation, the parameters found are suitable for the distribution in a domain of the amount of concentration of a material by means of the Cramer Rao limit and the value expected coefficients. With the non-linear technique used to find the optimal value of the constants, it was possible to observe the convergence of the coefficients at a given value thanks to the performance of this technique and the intrinsic characteristics of the database combined with a Gaussian normal distribution.