Multi-Year Survival Probability tPx Calculator
ConditionalwholeyearsurvivalΠpxfromactualsequenceqx,not constanthazardassumed. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.
Description
Multi-year survival combines conditional annual survival probabilities along an attained-age path.
Multi-year survival combines conditional annual survival probabilities along an attained-age path.1
This calculator multiplies the supplied interval factors without assuming that annual deaths are independent unconditional events.
When to use Multi-Year Survival Probability tPx Calculator
Use this tool to apply the stated multi-year survival probability tpx calculator operation with an explicit input and unit basis.
How to use Multi-Year Survival Probability tPx Calculator and how it works
- Establish the measurement basis and units described above.
- Enter actualAnnualQx, actualYearCount and run the tool.
- Read result.conditionalProbability 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 |
|---|---|---|---|
| actualAnnualQx | Nonempty sequence of conditional annual death probabilities in attained-age order. | array of number | required; dense; align related rows as specified; further conditions in the algorithm |
| actualYearCount | Year Count. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; further conditions in the algorithm |
Require a nonempty qx table with all entries in [0,1] and integer year count 0 through its length. For the leading intervals accumulate log1p(−qx) and exponentiate, returning zero directly when a selected qx is one; zero years returns one.
tpx = product of (1−qx[i]) for i=0…t−1 Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.conditionalProbability | Conditional multi-year death or survival probability under the supplied qx path. | number |
{
"input": {
"actualAnnualQx": [
0.1,
0.2
],
"actualYearCount": 2
},
"output": {
"result": {
"conditionalProbability": 0.72
}
}
}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 Multi-Year Death Probability tQx Calculator. A multi-year death probability is the complement of survival through successive conditional annual mortality intervals.
For a related operation, use Deferred Mortality Probability Calculator. A deferred mortality probability covers survival through a waiting period followed by death within a later coverage period.
References
Similar or alternative tools
- Multi-Year Death Probability tQx Calculator
A multi-year death probability is the complement of survival through successive conditional annual mortality intervals.
- Deferred Mortality Probability Calculator
A deferred mortality probability covers survival through a waiting period followed by death within a later coverage period.