Estimation of the Weibull Distribution Form Parameter as a Function of the Scale Parameter by the Percentile Method

Abstract

Among the probability density functions that estimate and project diametric distributions, the Weibull function is one of the most studied, and the percentile method is an alternative approach for estimating its parameters, with different deduction methods for calculating the location, scale, and shape parameters; in addition, of these parameters, some require iteration between formulas. In this study, the percentile method was used, and a function was established between the shape parameter, the asymptotic percentiles, and the scale parameter. This function was tested with continuous forest inventory (CFI) data of a Khaya grandifoliola stand and Eucalyptus spp. in integrated forest-livestock-forest (IFLF) systems, and the function was also validated based on distributions designed by the application of a recovery methodology for determining forest growth and production (FG&P) parameters. The results showed an exact correlation when compared with the parameters calculated by the percentile method. This function using the percentile method, due to its practicality, may be an alternative for obtaining the shape parameter in FG&P methodologies.