Data Analysis and Applications 1

11Estimation of a Two-Variable Second-Degree Polynomial via Sampling

In various fields of environmental and agriculture sciences, the estimation of two-variable second-degree polynomial coefficients via sampling is of major importance, as it gives very useful information. In this chapter, we propose a very simple and very low budget systematic sampling plan for the estimation of the coefficients A, B, C, D, E and H of the polynomial f(x, y) = (Ax² + By² + Cxy + Dx + Ey + H)^–1, which is sometimes found to be a probability density function. The above polynomial is defined on a domain D = [a, b] × [c, d], which can be represented by the domain D = [0, 1] × [0,1] for convenience. Numerical methods, such as Simpson’s rule, are applied. The comparison between means of both estimated and theoretic functions is used to confirm the accuracy of the results. The stability of the numerical methods allows us to get results with very good accuracy for small sample sizes. Illustrative examples are given in the following.

11.1. Introduction

All across the world, people are facing a wealth of environmental problems every day. Point-source pollutants have a major impact on environmental concentrations on a local scale and also contribute to the concentrations on a larger regional scale (van Leeuwen 2010). In accordance with the U.S. Environmental Protection Agency (EPA), point-source pollution is defined as “any single identifiable source of pollution from which pollutants are discharged, such ...