Weibull Diameter Distribution
Predict Weibull diameter-class count inventory under supplied shape/scale, retaining below/above surveyed class tails; not random sampling or inferred stand-table coefficients.
Description
A Weibull diameter distribution allocates expected stems to diameter classes.
A Weibull diameter distribution allocates expected stems to diameter classes. Explicit outside-class tails keep the modeled count inventory complete.1
Predict Weibull diameter-class count inventory under supplied shape/scale, retaining below/above surveyed class tails; not random sampling or inferred stand-table coefficients.
When to use Weibull Diameter Distribution
Use this tool to predict Weibull diameter-class count inventory under supplied shape/scale, retaining below/above surveyed class tails; not random sampling or inferred stand-table coefficients.
Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.
How to use Weibull Diameter Distribution and understand its results
- Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.
- Enter diameterClassEdgesCm, weibullScaleCm, weibullShape, standStemCount using the field table and calculation rules, then run the tool.
- Read expectedClassStemCounts, expectedBelowFirstClassStemCount, expectedAboveLastClassStemCount. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| diameterClassEdgesCm | Diameter class edges cm | list of number | Required |
| weibullScaleCm | Weibull scale cm | number | Required |
| weibullShape | Weibull shape | number | Required |
| standStemCount | Stand stem count | integer | Required |
Use positive scale cm and shape, nonnegative integer total stems and increasing nonnegative class edges. Evaluate stable hazard differences with expm1, retaining zero survival at saturated hazards. Return continuous expected class counts and counts below the first/above the last edge.
Each sequence checked for increasing order must contain at least two strictly increasing values.
class count=N exp(−Hlow)[1−exp(−(Hhigh−Hlow))], H(d)=(d/scale)^shape Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| expectedClassStemCounts | Expected class stem counts | list of number |
| expectedBelowFirstClassStemCount | Expected below first class stem count | number |
| expectedAboveLastClassStemCount | Expected above last class stem count | number |
{
"input": {
"diameterClassEdgesCm": [
0,
10,
20
],
"weibullScaleCm": 10,
"weibullShape": 1,
"standStemCount": 100
},
"output": {
"expectedClassStemCounts": [
63.212055882855765,
23.254415793482963
],
"expectedBelowFirstClassStemCount": 0,
"expectedAboveLastClassStemCount": 13.53352832366127
}
}Limitations and assumptions
Parameters are supplied, not fitted. Expected counts need not be integers and do not represent random draws.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Thinning Q-Factor Diameter Step: Normalize caller descending geometric q targets over equally spaced diameter classes, conserving supplied total density; these are continuous planning targets, not actual integer trees or an ecological prescription. For a complementary task, use Self Thinning Slope: Fit log mean-stem dry mass versus log stem density to observed self-thinning samples; unlike Reineke DBH stand density, no fixed -3/2 slope or maximum-density relationship is imposed.
References
-
Weibull Diameter Distribution — tool.io
Similar or alternative tools
- Thinning Q-Factor Diameter Step
Normalize caller descending geometric q targets over equally spaced diameter classes, conserving supplied total density; these are continuous planning targets, not actual integer trees or an ecological prescription.
- Self Thinning Slope
Fit log mean-stem dry mass versus log stem density to observed self-thinning samples; unlike Reineke DBH stand density, no fixed -3/2 slope or maximum-density relationship is imposed.