Modelling Tree Diameter Distribution With a Case Study from Garhbeta Sal Coppice Forest, Paschim Medinipur District, West Bengal

In forestry, statistical modelling has long been an effective tool in quantitative assessment of tree sizes using 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 Paschim Medinipur district, West Bengal. Thus, a comprehensive analysis of several descriptive and inferential statistics is provided here to identify the best-fit probability distribution in tree diameter estimation. The sample dataset comprises tree diameters (22 cm-44 cm) of 80 randomly selected sal trees, aged between 40-50 years. Twelve candidate probability distributions are evaluated in this study. The Maximum Likelihood Estimation (MLE) method is used for parameter estimation. Results from two goodness-of-fit criteria reveal that (i) the exponentiated exponential distribution provides the best fit, (ii) the Frechet (inverse Weibull), 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, some theoretical issues related to the selection of appropriate models are discussed. However, further studies encompassing multi-variable tree diameter data are recommended to strengthen the modelling results towards commercial timber production assessment in forests.