A new parameterization of Johnson's SB distribution with application to fitting forest tree diameter data

The SB distributional model of Johnson's 1949 paper was introduced by a transformation to normality, that is, z ~ N(0, 1), consisting of a linear scaling to the range (0, 1), a logit transformation, and an affine transformation, z = γ + δu. The model, in its original parameterization, has often been used in forest diameter distribution modelling. In this paper, we define the SB distribution in terms of the inverse transformation from normality, including an initial linear scaling transformation, u = γ′ + δ′z (δ′ = 1/δ and γ′ = �γ/δ). The SB model in terms of the new parameterization is derived, and maximum likelihood estimation schema are presented for both model parameterizations. The statistical properties of the two alternative parameterizations are compared empirically on 20 data sets of diameter distributions of Changbai larch (Larix olgensis Henry). The new parameterization is shown to be statistically better than Johnson's original parameterization for the data sets considered here.

Semi-Parametric Analysis of Extreme Forest Fires

Forest fires can cause extensive damage to natural resources and properties. They can also destroy wildlife habitat, affect the forest ecosystem and threaten human lives. In this paper incidences of extreme wildland fires are modelled by a point process model which incorporates time-trend. A model based on a generalised Pareto distribution is used to model data on acres of wildland burnt by extreme fire in the US since 1825. A semi-parametric smoothing approach, which is very useful in exploratory analysis of changes in extremes, is illustrated with the maximum likelihood method to estimate model parameters.