Comparison of the goodness of fit of the Langmuir isotherm

Abstract

The objective of this work was to compare the estimates quality of the Langmuir

isotherm parameters obtained via Gauss-Newton method and Levenberg-Marquardt method. To

compare the estimates of the model parameters obtained by these two iterative numerical methods,

were simulated 1000 data sets, with concentrations ranging from 0.5 to 100 and sample sizes of

9, 12, 15, 16, 30 and 60 from the Langmuir isotherm parameters with

K

= 2

.

96

and

M

= 0

.

91

.

For the evaluation of estimates, the accuracy and precision of the Langmuir isotherm estimates

by the Gauss-Newton and the Levenberg-Marquardt methods were analyzed. Accuracy was as-

sessed using the average relative bias and the approximate accuracy by the mean square error.

The results suggest that the two estimation methods have similar precision and accuracy to the

sizes of the samples studied. How is it possible that the Gauss - Newton don’t converge or that

the process is interrupted by the lack of unique solution of the linear system that determines the

update of the parameter values, it is concluded the Levenberg-Marquardt method is more suitable

for estimating the Langmuir isotherm parameters.