Qx to Mx Converter

Actual inversecentralratemx=qx/[n−(n−a)qx],independenta/no constanthazardassumption. Actual independently applicable qualified life-table/model/rate assumptions,not a diagnosis,individual death prediction,published mortalitytable,contractquote or guaranteed financialresult.

Description

A mortality probability qx and central death rate mx use different denominators.

A mortality probability qx and central death rate mx use different denominators.^[1]

This converter uses a supplied interval length and mean time lived within the interval by those who die, rather than assuming the usual half-year value.

When to use Qx to Mx Converter

Use this tool to apply the stated qx to mx converter operation with an explicit input and unit basis.

How to use Qx to Mx Converter and how it works

Establish the measurement basis and units described above.
Enter actualIntervalQx, actualIntervalYears, callerIndependentMeanYearsLivedByDecedents 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
actualIntervalQx	Interval Qx. Units, ordering and applicable branch are specified in the algorithm.	number	required; finite; 0–1 inclusive; further conditions in the algorithm
actualIntervalYears	Interval Years. Units, ordering and applicable branch are specified in the algorithm.	number	required; finite; strictly positive; further conditions in the algorithm
callerIndependentMeanYearsLivedByDecedents	Average years lived in the interval by those dying, from zero through interval length.	number	required; finite; nonnegative; further conditions in the algorithm

Require q in [0,1], interval n>0 and mean death-time a in [0,n]. Divide q by n−(n−a)q and reject a nonpositive denominator, including q=1 with a=0.

mx = qx/[n−(n−a)qx]

Apply the declared units, ordering and branch conditions.

Output field	Meaning	Value type
result	Object containing the declared output fields.	object
result.value	Central death rate per year under the supplied interval-exposure convention.	number

json

{
  "input": {
    "actualIntervalQx": 0.25,
    "actualIntervalYears": 2,
    "callerIndependentMeanYearsLivedByDecedents": 1
  },
  "output": {
    "result": {
      "value": 0.14285714285714285
    }
  }
}

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 Mx to Qx Converter. A central death rate can be converted to a cohort death probability only with an interval-exposure convention.

For a related operation, use Central Death Rate Mx Calculator. A central death rate uses person-years of exposure rather than the cohort present at interval start.

References

Qx to Mx Converter — tool.io

Similar or alternative tools

Mx to Qx Converter
A central death rate can be converted to a cohort death probability only with an interval-exposure convention.
Central Death Rate Mx Calculator
A central death rate uses person-years of exposure rather than the cohort present at interval start.