The bivariate Power-Normal and the bivariate Johnson’s System bounded distribution in forestry, including height curves. Supplementary material.
Bibliographic record
Abstract
This document contain supplementary material concerning two published papers: Mønness, E. 2011b. The Power-Normal Distribution: Application to forest stands. Canadian Journal of Forest Research 41(4): 707-714. doi: 10.1139/X10-246.\nMønness, E 2014. The bivariate Power-Normal and the bivariate Johnson’s System bounded distribution in forestry, including height curves. Canadian Journal of Forest Research. 2015 Supplementary material to the above article; SAS programs and computing details are found in Mønness, E. 2011a. The Power-Normal Distribution and Johnsons System bounded distribution: Computing details and programs. Available from http://hdl.handle.net/11250/133513 3] .\nFrom published abstracts: The Power-Normal (PN) distribution, originated from the inverse Box-Cox transformation, is presented and some possibilities in forest research are explored. The Power-Normal achieve shapes, by a Skewness * Kurtosis value, common to diameters and heights of forest stands. The estimation of the parameters by maximum likelihood is straightforward with good numerical properties. The shapes achieved by PN are very diverse even with only three parameters: The Johnson System bounded distribution (SB), also used in forestry, can encounter numerical problems with maximum likelihood estimation. The PN distribution is seen to give good estimates of diameter and height distributions, judged by the Kolmogorov-Smirnov statistic and visual inspection. It seems to perform better than the SB, especially on heights.\nA bivariate diameter and height distribution yields a unified model of a forest stand. The bivariate Johnson’s System bounded distribution and the bivariate power-normal distribution are explored. The power-normal originates from the well-known Box-Cox transformation. As evaluated by the bivariate Kolmogorov-Smirnov distance, the bivariate power-normal distribution seems to be superior to the bivariate Johnson’s System bounded distribution.\nThe conditional median height given the diameter is a possible height curve and is compared with a simple hyperbolic height curve. Evaluated by the height deviance, the hyperbolic function yields the best height prediction. A close second is the curve generated by a bivariate power-normal distribution. Johnson’s System bounded distributions suffer from the sigmoid shape of the association between height and diameter.\nThe data is from Vestjordet, E. 1977. Precommercial thinning of young stands of Scots Pine and Norway Spruce I: Data stability, dimension distribution etc. Medd. Nor. inst. skogforsk 33(9): 1-436.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.102 | 0.023 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".