Generalized Least Absolute Deviation Method and Its Application in Biology

Extend the Least Absolute Deviation criterion which is zero deviation character {y_j-f(x_j, a*) = 0, j = 1,...., n, Σ_j= |y_i-f(x_i, a*) = min, keep zero deviation, change different fitting conditions, constitutes the generalized Least Absolute Deviation method. In the absolute value, two generalized Least Absolute Deviation criteria are: Maximum relative error minimization: {y_j-f(x_j, a*) = 0, j = 1,...., n, max _1≤j≤m |(y_i-f(x_i, a*))/y_i| = min. Sum of relative error minimization: {y_j-f(x_j, a*) = 0, j = 1,...., n, Σ_i=1 |(y_i-f(x_i, a*))/y_i| = min. These guidelines apply not only to linear fit is also applied to nonlinear fitting, applies not only to a single variable, also applies to many variables, to enrich the content of least-squares best approximation. In Biology , the creation of life from have no to have, changes in organisms from small to large, this change is very great. The method of curve fitting with the metric of relative value, applied to a description of these changes, can overcome some shortcomings in the past, the article around these new criterions provides details of the application.