Funções de afilamento não-lineares por GAMLSS

Abstract

This study was developed based on the diameter and height measurements of 40 Eucalyptus sp. trees, collected from a property in the south-central region of the state of Mato Grosso, using the Smalian method of cubing. The taper function is used in forest engineering as it describes how the diameter of trees varies in relation to trunk height. This description is used to understand tree growth over time and to plan how to manage and utilize available forest resources efficiently. The Generalized Additive Model for Location, Scale, and Shape (GAMLSS) can model not only the location and scale of the data but also its shape, offering greater flexibility in statistical analysis and interpretation of results compared to other regression models. Taper models by Kozak (2004), Max & Burkhart (1976), Clark III, Souter & Schlaegel (1991), and Demaerschalk (1972) were used to describe the longitudinal profile of the trees. These models were combined with NO 1 , LO 2 , TF2 3 , JSU 4 , and SST 5 distributions to estimate the diameters of Eucalyptus sp. trees. The linear predictors were defined such that µ was a function of taper, σ was simple linear, while ν and τ were kept constant. Analyses were conducted to verify normality in each taper model, as well as their behavior concerning the chosen data distribution family, evaluated through graphical methods. The comparison between the taper models and the distribution families was carried out by applying weights to each calculated accuracy. The results of the study highlighted the effectiveness of the combination between taper functions and the GAMLSS model in estimating the diameters of Eucalyptus sp. trees. However, emphasis was placed on the segmented equation model of Clark, Souter, and Schlaegel (1991) with JSU and SST distributions, which proved to be the most accurate for estimating the diameters of Eucalyptus sp. trees among the taper functions and distributions used in this study.