Modelling Tree Diameter Distributions in Forests:A Case Study from Garhbeta (West Bengal) Sal Coppice Forest

Abstract

In forestry, statistical modelling has long been an effective tool in quantitative assessment of tree sizes using various probability distributions on tree diameters at breast height (dbh). It is however still unclear that which family of probability distributions, viz., symmetric, skewed, or heavy-tailed models are more flexible to this end, especially in forests within a small area like Garhbeta sal (Shorea robusta) coppice forest of West Medinipur district, West Bengal. Here we provide a comprehensive analysis of several descriptive and inferential statistics to identify the best-fit probability distribution in tree diameter estimation. Our sample data set comprises tree diameters (22-44 cm) of 80 randomly selected sal trees, aged between 40-50 years. Twelve candidate probability distributions, namely, exponential, exponentiated exponential, Frechet (inverse Weibull), gamma, Gaussian, inverse Gaussian, Levy, lognormal, Maxwell, Pareto, Rayleigh and Weibullare were used in this study. The Maximum Likelihood Estimation (MLE) method is applied for the parameter estimation, whereas the Fisher Information Matrix (FIM) based surrogate approach is used for uncertainty analysis. We determine the best-fit distribution(s) from two goodness-of-fit tests: Akaike Information Criterion (AIC) and Kolmogorov-Smirnov (K-S) minimum distance criterion. Results reveal that (i) the exponentiated exponential distribution provides the best fit, (ii) the Frechet, gamma, Gaussian, inverse Gaussian, lognormal and Weibull distributions provide the intermediate fit and (iii) the rest, namely exponential, Levy, Maxwell, Pareto and Rayleigh distributions fit poorly to the observed tree diameters in the study area. Finally, we discuss some theoretical issues related to the selection of appropriate models. However, further studies encompassing multi-variable tree diameter data are recommended to arrive at a reasonably acceptable probability model useful for assessing timber production in forests.