Nonlinear regression approach to estimating Johnson S(B) parameters for diameter data

Abstract

A nonlinear regression approach is proposed to estimate the parameters of the Johnson S(B) distribution. This method was compared to five other methods; these were the four percentile points method, the Knoebel-Burkhart method, the linear regression method, the maximum likelihood (Newton-Raphson) method, and the modified maximum likelihood method through simulation. The performance of the nonlinear regression method was also investigated by using the real diameter data collected from 20 even-aged sample plots of the Acacia mangium Willd. plantation in Sandakan, Sabah, measured annually from age 2 to 8 years. Goodness-of-fit tests based on empirical distribution function (namely the Kolmogorov-Smirnov statistic, Cramer- von Mises statistic, and the Anderson-Darling statistic) were used in selecting the most superior parameter estimation method. Results suggested that the nonlinear regression method was superior for estimating parameters of the Johnson S(B) distribution for diameter data in terms of bias, root mean square error, and goodness-of-fit tests.