Dependent to Independent Decrement Converter
Recover the single-cause independent annual decrement rate from its dependent multiple-decrement table rate assuming constant forces within the year.
Description
Convert a cause-specific dependent multiple-decrement rate to its independent single-decrement rate under constant forces.
Dependent to Independent Decrement Converter helps you convert a cause-specific dependent multiple-decrement rate to its independent single-decrement rate under constant forces.
Use this conversion when a multiple-decrement table reports the observed probability for one cause in the presence of competing exits, but a corresponding single-cause probability is needed. Common causes include death, disability, withdrawal, and retirement.
When to use Dependent to Independent Decrement Converter
Use this conversion when a multiple-decrement table reports the observed probability for one cause in the presence of competing exits, but a corresponding single-cause probability is needed. Common causes include death, disability, withdrawal, and retirement.1
How the calculation works
The method converts total dependent survival into a total force, allocates that force to the selected cause in proportion to its dependent rate, and converts the cause-specific force back to an annual independent probability.
q′j = 1 − (1 − Σqj)^(qj / Σqj) 1Inputs and interpretation
Supply all dependent annual rates from the same table row and select a one-based cause index. Rates must be nonnegative and their total must be strictly between zero and one.
Assumptions and limitations
The conversion depends on constant forces within the year. Different assumptions about the timing or interaction of decrements can produce different independent rates. Do not mix rates from different populations, periods, or table bases.
References
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Supplementary Notes for Actuarial Mathematics for Life Contingent Risks — Society of Actuaries