Gompertz Law Force of Mortality Calculator
Conditional Gompertz law μ(x)=B c^x for independently calibrated B>0, c>1, in inverse years, with integrated next-year hazard and exp(−hazard) survival. These are explicit actuarial model assumptions, not observed individual death probability, diagnosis, life expectancy, clinical advice or a published mortality table.
Description
A force of mortality is an instantaneous actuarial rate whose integral determines modeled survival.
A force of mortality is an instantaneous actuarial rate whose integral determines modeled survival.1
This tool evaluates an independently calibrated increasing Gompertz model and its next-year hazard without predicting an individual's death.
When to use Gompertz Law Force of Mortality Calculator
Use this tool to evaluate an independently calibrated increasing Gompertz model and its next-year hazard without predicting an individual's death.
How to use Gompertz Law Force of Mortality Calculator and how it works
- Establish the observations, units, reference context and assumptions described below.
- Enter callerCalibratedBaselineForcePerYear, callerCalibratedAnnualGrowthFactor, ageYears and run the tool.
- Read result.conditionalForcePerYear, result.forceDoublingAgeIntervalYears, result.conditionalIntegratedNextYearHazard, result.conditionalNextYearSurvival using the meanings and sign conventions below.
- Correct any rejected inputs and rerun; independently review the result under the stated scope.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerCalibratedBaselineForcePerYear | Independently calibrated positive Gompertz baseline B in inverse years. | number | Required; finite; strictly positive; branch conditions below |
| callerCalibratedAnnualGrowthFactor | Independently calibrated dimensionless annual growth factor c, strictly greater than one. | number | Required; finite; branch conditions below |
| ageYears | Modeled age x in years from 0 to 150 inclusive; fractional years allowed. | number | Required; finite; branch conditions below |
Supply positive calibrated baseline force B in inverse years, annual growth factor c>1 and age x from 0 to 150 years inclusive; fractional ages are allowed. Let l=ln(c), evaluate mu=exp(ln(B)+x*l), next-year integrated hazard H=mu*expm1(l)/l, doubling interval ln(2)/l and survival exp(-H). Nonfinite intermediates are rejected, but survival may underflow to zero. This zero-Makeham increasing Gompertz model does not fit data or give an observed individual risk.
mu=B*c^x; doublingYears=ln(2)/ln(c); nextYearHazard=mu*(c-1)/ln(c); nextYearSurvival=exp(-nextYearHazard) Use the stated ordering, units and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the fields below. | object |
| result.conditionalForcePerYear | Conditional instantaneous mortality force at age x, in inverse years. | number |
| result.forceDoublingAgeIntervalYears | Modeled age interval in years over which the force doubles. | number |
| result.conditionalIntegratedNextYearHazard | Dimensionless cumulative hazard over the next one-year interval. | number |
| result.conditionalNextYearSurvival | Conditional exp(-next-year hazard) survival fraction; may underflow to zero. | number |
{
"input": {
"callerCalibratedBaselineForcePerYear": 0.001,
"callerCalibratedAnnualGrowthFactor": 2,
"ageYears": 3
},
"output": {
"result": {
"conditionalForcePerYear": 0.008000000000000004,
"forceDoublingAgeIntervalYears": 1,
"conditionalIntegratedNextYearHazard": 0.011541560327111712,
"conditionalNextYearSurvival": 0.9885247879806346
}
}
}Limitations and assumptions
The calculation depends on independently established observations, coefficients and the matching units. It does not collect data, choose a treatment or target, establish model applicability or provide a validated forecast. Interpret its result within the branch conditions and assumptions above.
Supply explicit values and dense aligned arrays. Unexpected fields, wrong types and nonfinite scalar values are rejected; fixed-token, alignment and other branch conditions are explained above. A successful false flag, empty match list or unknown-evidence list differs from an input error. Extremely large inputs or nonrepresentable results may fail.
Alternative or Complementary methods
Use Constant Force Fractional Survival for a related operation: Interpolate survival within the year under a constant force of mortality.
Use Hazard Consistency Checker for a related operation: Compare an annual event probability with the probability implied by a constant annual hazard rate.
References
Similar or alternative tools
- Constant Force Fractional Survival
Interpolate survival within the year under a constant force of mortality.
- Hazard Consistency Checker
Compare an annual event probability with the probability implied by a constant annual hazard rate.