Modelos simétricos transformados não-lineares com diferentes distribuições dos erros: aplicações em ciências florestais

Abstract

Historically, the wood of the eucalyptus is used for the most varied applications, such as; firewood, charcoal, cellulose, railway sleepers, posts for electrification, bark to tan leather, essential oils, civil construction, etc. The Gypsum Pole of Araripe in Pernambuco is a great firewood consumer for the gypsum production. Due to great need to find economical and environmental alternatives for the area, the sustainable production of eucalyptus that is a fast growth tree with great versatility has an important role. In the planning of the sustainable forest management there is a variable of extreme importance: the growth. To model the growth is fundamental in the prognosis of the productivity, site quality and dynamics of populations. Usually, the growth curves are fitted through nonlinear models developed empirically to relate, for instance, height and age. The Chapman-Richards model is a nonlinear model frequently used to model forest growth. In studies of this type, in general, it is assumed that the errors follow approximately the normal distribution. However, to model the growth assuming that the errors have a normal distribution is quite sensitive to atypical values that can happen, and generate bad estimates of the parameters. To correct that problem a new class of transformed symmetrical models was developed considering for the errors symmetrical continuous distributions with heavier tails than the normal distribution and allowing a possible nonlinear structure for the mean. With the expectation of obtaining better estimates of eucalyptus growth, it was applied to the Chapman-Richards model the following distributions of the errors: normal, t of Student, Cauchy, exponential potency, logistics I and logistics II. The t distribution of Student with 2 degrees of freedom was the most efficient to estimate height and circumference growth of eucalyptus in the Gypsum Pole of Pernambuco.