Commutation Function Cx Calculator
CommutationC_x=v^(x+1)d_xendyearmortalitydiscount,notv^xD_x. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Description
The death commutation value Cx discounts interval deaths to the end of the age interval.
The death commutation value Cx discounts interval deaths to the end of the age interval.1
This calculator applies an annual discount factor to a supplied lowercase dx death count.
When to use Commutation Function Cx Calculator
Use this tool to apply the stated commutation function cx calculator operation with an explicit input and unit basis.
How to use Commutation Function Cx Calculator and how it works
- Establish the measurement basis and units described above.
- Enter callerActualAnnualDiscountFactor, actualAttainedAge, actualLifeTableIntervalDeaths and run the tool.
- Read result.value using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerActualAnnualDiscountFactor | Annual Discount Factor. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; 0–1 inclusive; further conditions in the algorithm |
| actualAttainedAge | Attained Age. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; integer from 0 to 1000000; further conditions in the algorithm |
| actualLifeTableIntervalDeaths | Life Table Interval Deaths. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; nonnegative; further conditions in the algorithm |
Require v in [0,1], integer age 0–1,000,000 and nonnegative interval deaths dx. Multiply by v^(x+1); the extra exponent implements end-of-interval timing.
Cx = v^(x+1) dx Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.value | Death commutation value on the supplied life-table radix. | number |
{
"input": {
"callerActualAnnualDiscountFactor": 0.5,
"actualAttainedAge": 2,
"actualLifeTableIntervalDeaths": 10
},
"output": {
"result": {
"value": 1.25
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A returned boolean, signed difference or tied result follows the stated convention; an input error instead means the required input contract was not satisfied. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Commutation Function Mx Calculator. The actuarial M commutation function sums death commutation values from the current age onward.
For a related operation, use Commutation Function Dx Calculator. The survivor commutation value Dx combines an attained-age discount power with a life-table survivor count.
References
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Commutation Function Cx Calculator — tool.io
Similar or alternative tools
- Commutation Function Mx Calculator
The actuarial M commutation function sums death commutation values from the current age onward.
- Commutation Function Dx Calculator
The survivor commutation value Dx combines an attained-age discount power with a life-table survivor count.