Stand Diameter Distribution Modeling and Prediction Based on Maximum Entropy Principle

Yuling Chen,Zhiqiang Min,Baoguo Wu

doi:10.3390/f10100859

Abstract

Research Highlights: Improving the prediction accuracy represents a popular forest simulation modeling issue, and exploring the optimal maximum entropy (MaxEnt) distribution is a new effective method for improving the diameter distribution model simulation precision to overcome the disadvantages of Weibull. Background and Objectives: The MaxEnt distribution is the closest to the actual distribution under the constraints, which are the main probability density distributions. However, relatively few studies have addressed the optimization of stand diameter distribution based on MaxEnt distribution. The objective of this study was to introduce application of the MaxEnt distribution on modeling and prediction of stand diameter distribution. Materials and Methods: The long-term repeated measurement data sets consisted of 260 diameter frequency distributions from China fir (Cunninghamia lanceolate (Lamb.) Hook) plantations in the southern China Guizhou. The Weibull distribution and the MaxEnt distribution were applied to the fitting of stand diameter distribution, and the modeling and prediction characteristics of Weibull distribution and MaxEnt distribution to stand diameter distribution were compared. Results: Three main conclusions were obtained: (1) MaxEnt distribution presented a more accurate simulation than three-parametric Weibull function; (2) the Chi-square test showed diameter distributions of unknown stands can be well estimated by applying MaxEnt distribution based on the plot similarity index method (PSIM) and Weibull distribution based on the parameter prediction method (PPM); (3) the MaxEnt model can deal with the complex nonlinear relationship and show strong prediction ability when predicting the stand distribution structure. Conclusions: With the increase of sample size, the PSIM has great application prospects in the dynamic prediction system of stand diameter distribution.

Highlights

Weibull distribution based on the parameter prediction method (PPM); (3) the maximum entropy (MaxEnt) model can deal with the complex nonlinear relationship and show strong prediction ability when predicting the stand distribution structure
According to the characteristics of maximum entropy model belonging to the machine learning algorithm, this paper presents a dynamic prediction method of stand diameter distribution by plot similarity index method
For the MaxEnt distribution equation, it can be seen from the residual sum of square (RSS) and mean square error (MSE) that the fitting results of the two-parameter MaxEnt model (m = 1) and the three-parameter MaxEnt model (m = 2) were poor, and that the fitting results of the four-parameter

Summary

Introduction

A variety of probability density distribution functions have been used to describe the stand diameter structure, such as normal distribution, lognormal distribution, beta distribution [4], Johnson’s SB distribution [5], distribution and Weibull distribution [2,6,7,8,9,10,11,12,13]. These distribution functions have demonstrated their respective advantages under different regional conditions and tree types, among which the Weibull distribution function was characterized by great adaptability and Forests 2019, 10, 859; doi:10.3390/f10100859 www.mdpi.com/journal/forests. In the dynamic prediction of stand diameter distribution, the main methods have been parameter prediction method (PPM) [27,28,29,30], parameter recovery method (PRM) [31,32,33] and generalized linear model [34,35,36]

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Methods

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Discussion

Conclusion