Rennolls, Keith and Wang, Mingliang (2005) A new parameterization of Johnson's SB distribution with application to fitting forest tree diameter data. Canadian Journal of Forest Research, 35 (3). pp. 575-579. ISSN 0045-5067 (Print), 1208-6037 (Online) (doi:https://doi.org/10.1139/x05-006)

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	Johnson's SB distributional model, forest tree diameter data
Subjects:	Q Science > QA Mathematics S Agriculture > SD Forestry
Pre-2014 Departments:	School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Computer Science School of Computing & Mathematical Sciences > Statistics & Operational Research Group
Related URLs:	Publisher
Last Modified:	14 Oct 2016 09:02
URI:	http://gala.gre.ac.uk/id/eprint/853

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