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Related Concept Videos

Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Related Experiment Video

Updated: May 11, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

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Published on: July 3, 2020

Stand diameter distribution modelling and prediction based on Richards function.

Ai-guo Duan1, Jian-guo Zhang, Xiong-qing Zhang

  • 1State Key Laboratory of Tree Genetics and Breeding, Research Institute of Forestry, Chinese Academy of Forestry, Beijing, China.

Plos One
|May 3, 2013
PubMed
Summary
This summary is machine-generated.

The R distribution accurately models Chinese fir stand diameter distribution, outperforming the Weibull function. This model aids in predicting forest stand characteristics using stand age or quadratic mean diameter.

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Last Updated: May 11, 2026

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Area of Science:

  • Forestry Science
  • Quantitative Ecology
  • Statistical Modeling

Background:

  • Accurate modeling of stand diameter distribution is crucial for sustainable forest management.
  • Traditional models like the Weibull function have limitations in capturing complex diameter distributions.
  • Chinese fir (Cunninghamia lanceolata) plantations are economically important in Southern China.

Purpose of the Study:

  • To introduce and evaluate the application of the Richards equation for modeling and predicting stand diameter distribution in Chinese fir plantations.
  • To compare the performance of the R distribution with the three-parametric Weibull function.
  • To assess methods for predicting diameter distributions of unknown stands.

Main Methods:

  • Utilized long-term repeated measurement data from 309 Chinese fir stands.
  • Estimated model parameters using Nonlinear Regression Method (NRM) and Maximum Likelihood Estimates Method (MLEM).
  • Employed Parameter Prediction Method (PPM) and Parameter Recovery Method (PRM) for predicting diameter distributions.

Main Results:

  • The R distribution provided a more accurate simulation of diameter distribution compared to the three-parametric Weibull function.
  • Parameters of the R distribution (p, q, r) were identified as scale, location, and shape parameters, respectively, showing strong relationships with stand characteristics.
  • The R distribution demonstrated good interpretability and accurately estimated diameter distributions of unknown stands with near 80% non-rejection rates.

Conclusions:

  • The R distribution is a superior model for simulating stand diameter distribution in Chinese fir plantations.
  • The parameters of the R distribution have theoretical significance and can be linked to stand characteristics.
  • The R distribution, particularly using PRM or combined PPM/PRM, effectively predicts diameter distributions of unknown stands, outperforming the Weibull function.