Body Size Frequency Log-Normal Fit Check
Summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality.
Description
A lognormal hypothesis concerns distribution in log size space.
A lognormal hypothesis concerns distribution in log size space. Empirical skewness and kurtosis summarize shape without constituting a formal fit test.
Summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality.
When to use Body Size Frequency Log-Normal Fit Check
Use this tool to summarize empirical population moments in log body-size space with a caller skewness screen; not a formal distribution goodness-of-fit test or proof of lognormality.
Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
How to use Body Size Frequency Log-Normal Fit Check and understand its results
- Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
- Enter bodySizes, callerMaximumAbsoluteLogSkewness using the field table and calculation rules, then run the tool.
- Read meanNaturalLogSize, populationLogStandardDeviation, populationLogSkewness, populationLogExcessKurtosis, withinCallerLogSkewnessScreen. 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 |
|---|---|---|---|
| bodySizes | Body sizes | list of number | Required |
| callerMaximumAbsoluteLogSkewness | Caller maximum absolute log skewness | number | Required |
Use at least three positive sizes with nonzero log variance and nonnegative maximum absolute skewness. Compute population log mean, SD, skewness and excess kurtosis; compare skewness inclusively.1
log skewness = mean((ln(size)−mean)³)/population log variance^(3/2) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| meanNaturalLogSize | Mean natural log size | number |
| populationLogStandardDeviation | Population log standard deviation | number |
| populationLogSkewness | Population log skewness | number |
| populationLogExcessKurtosis | Population log excess kurtosis | number |
| withinCallerLogSkewnessScreen | Within caller log skewness screen | boolean |
{
"input": {
"bodySizes": [
1,
2.718281828459045,
7.38905609893065
],
"callerMaximumAbsoluteLogSkewness": 0.5
},
"output": {
"meanNaturalLogSize": 1,
"populationLogStandardDeviation": 0.816496580927726,
"populationLogSkewness": 0,
"populationLogExcessKurtosis": -1.5,
"withinCallerLogSkewnessScreen": true
}
}Limitations and assumptions
Passing the screen does not prove lognormality or provide a goodness-of-fit p-value.
Numbers and computed results must be finite; overflow 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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Cope's Rule Size Trend Slope: Fit signed log body-size trend on an explicit increasing forward-time axis and report multiplicative change; sampling, taxonomic replacement and phylogeny can confound any Cope-rule interpretation. For a complementary task, use Raup Coil Log-Spiral W-D Parameters Solver: Fit logarithmic whorl radial expansion per full turn and report Raup-style D under explicit inner/outer radius convention; only W/D are estimated, not generating shape, axial translation or 3D reconstruction.
References
-
Body Size Frequency Log-Normal Fit Check — tool.io
Similar or alternative tools
- Cope's Rule Size Trend Slope
Fit signed log body-size trend on an explicit increasing forward-time axis and report multiplicative change; sampling, taxonomic replacement and phylogeny can confound any Cope-rule interpretation.
- Raup Coil Log-Spiral W-D Parameters Solver
Fit logarithmic whorl radial expansion per full turn and report Raup-style D under explicit inner/outer radius convention; only W/D are estimated, not generating shape, axial translation or 3D reconstruction.