Open AccessEstimation of the parameters of the particular solution of a partial differential equation through Cramer Rao
Author(s) -
Fernando Mesa,
D M Devia,
Raydonal Ospina
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1671/1/012014
Subject(s) - mathematics , estimation theory , gaussian , probability density function , limit (mathematics) , partial differential equation , convergence (economics) , distribution (mathematics) , function (biology) , mathematical optimization , statistics , mathematical analysis , physics , quantum mechanics , evolutionary biology , economics , biology , economic growth
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.