Cohort Component Projection Calculator
One externally established cohort survival/aging transition plus independent births/net migration additions, population vector next=Tnow+additions. Not fit demographic rates or validated multi-year forecast.
Description
A cohort-component step applies survival and aging transitions to a population vector.
A cohort-component step applies survival and aging transitions to a population vector.1
Births and net migration enter as separately established additions for the same period. The calculation and input requirements are explained below.
When to use Cohort Component Projection Calculator
Enter 1–64 nonnegative initial cohort counts, an aligned square transition matrix and matching finite signed period additions.
How to use Cohort Component Projection Calculator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Cohort Component Projection Calculator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualInitialCohortCounts | Actual Initial Cohort Counts. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
| callerEstablishedNextPeriodTransitionMatrix | Caller Established Next Period Transition Matrix. Use the units and matching context stated in the calculation below. | array of array of number | Required; other constraints below |
| callerIndependentPeriodAdditions | Caller Independent Period Additions. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
Enter 1–64 nonnegative initial cohort counts, an aligned square transition matrix and matching finite signed period additions. Matrix entries must be fractions and each column sum at most 1+1e-9. Multiply each matrix row by the initial vector and add the corresponding addition. Reject negative projected counts. Fractional populations are accepted; rates are not fitted or iterated into a forecast.
nextCounts=T*initialCounts+periodAdditions Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.conditionalNextPeriodCohortCounts | Conditional Next Period Cohort Counts. Interpret its unit, sign, order or availability flag as explained above. | array of number |
{
"input": {
"actualInitialCohortCounts": [
10,
20
],
"callerEstablishedNextPeriodTransitionMatrix": [
[
0.5,
0
],
[
0.5,
1
]
],
"callerIndependentPeriodAdditions": [
1,
2
]
},
"output": {
"result": {
"conditionalNextPeriodCohortCounts": [
6,
27
]
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Life Table Survivorship Lx Calculator for a complementary operation: Life-table survivorship subtracts interval deaths from beginning survivors.
Use Life Expectancy at Birth Calculator for a complementary operation: Life expectancy at birth divides total life-table person-years by the starting radix.
References
-
Cohort Component Projection Calculator — tool.io
Similar or alternative tools
- Life Table Survivorship Lx Calculator
Life-table survivorship subtracts interval deaths from beginning survivors.
- Life Expectancy at Birth Calculator
Life expectancy at birth divides total life-table person-years by the starting radix.