Taphonomic Time Averaging Mixing Model Estimate
Combine supplied age-distribution components by the law of total variance, distinguishing within/between temporal mixing; no inferred depositional duration or deconvolved event dates.
Description
A mixed age distribution varies within components and between component means.
A mixed age distribution varies within components and between component means. The law of total variance separates those contributions.
Combine supplied age-distribution components by the law of total variance, distinguishing within/between temporal mixing; no inferred depositional duration or deconvolved event dates.
When to use Taphonomic Time Averaging Mixing Model Estimate
Use this tool to combine supplied age-distribution components by the law of total variance, distinguishing within/between temporal mixing; no inferred depositional duration or deconvolved event dates.
Prepare the fossil measurements or occurrence records and the chosen calibration parameters. Retain the stated coordinate, age and measurement conventions.
How to use Taphonomic Time Averaging Mixing Model Estimate 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 componentMeanAgesYears, componentAgeVariancesYearsSquared, mixtureWeights using the field table and calculation rules, then run the tool.
- Read mixtureMeanAgeYears, withinComponentVarianceYearsSquared, betweenComponentVarianceYearsSquared, mixtureAgeStandardDeviationYears. 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 |
|---|---|---|---|
| componentMeanAgesYears | Component mean ages years | list of number | Required |
| componentAgeVariancesYearsSquared | Component age variances years squared | list of number | Required |
| mixtureWeights | Mixture weights | list of number | Required |
Align means, nonnegative variances and nonnegative weights with positive total weight. Normalize weights and return mixture mean, both variance components and total standard deviation.1
Paired lists must be nonempty and have equal lengths.
total variance = weighted within variance + weighted squared deviations of component means Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| mixtureMeanAgeYears | Mixture mean age years | number |
| withinComponentVarianceYearsSquared | Within component variance years squared | number |
| betweenComponentVarianceYearsSquared | Between component variance years squared | number |
| mixtureAgeStandardDeviationYears | Mixture age standard deviation years | number |
{
"input": {
"componentMeanAgesYears": [
100,
200
],
"componentAgeVariancesYearsSquared": [
25,
100
],
"mixtureWeights": [
1,
3
]
},
"output": {
"mixtureMeanAgeYears": 175,
"withinComponentVarianceYearsSquared": 81.25,
"betweenComponentVarianceYearsSquared": 1875,
"mixtureAgeStandardDeviationYears": 44.22951503238533
}
}Limitations and assumptions
Supplied components are not deconvolved event dates or an inferred depositional duration.
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.
Alternative or Complementary methods
Use Stratigraphic Range Extent: Summarize observed section-position span and endpoint measurement uncertainty, not true taxon duration; positions share a caller increasing chronological/section convention. For a complementary task, use Death Assemblage to Living Community Offset Corrector: Invert a supplied identifiable nonnegative living-to-death preservation/mixing response and report reconstruction residual; negative physical solutions error rather than clipping, and response is not inferred from one assemblage.
References
Similar or alternative tools
- Stratigraphic Range Extent
Summarize observed section-position span and endpoint measurement uncertainty, not true taxon duration; positions share a caller increasing chronological/section convention.
- Death Assemblage to Living Community Offset Corrector
Invert a supplied identifiable nonnegative living-to-death preservation/mixing response and report reconstruction residual; negative physical solutions error rather than clipping, and response is not inferred from one assemblage.