Independent to Dependent Decrement Converter
Convert an independent annual decrement rate into its dependent multiple-decrement table rate assuming constant forces within the year.
Description
Convert independent single-decrement annual rates into a cause-specific dependent rate under constant forces.
Independent to Dependent Decrement Converter helps you convert independent single-decrement annual rates into a cause-specific dependent rate under constant forces.
Use this conversion to construct a multiple-decrement table rate when separate single-cause probabilities are available. It accounts for the fact that competing causes reduce the opportunity for the selected cause to occur.
When to use Independent to Dependent Decrement Converter
Use this conversion to construct a multiple-decrement table rate when separate single-cause probabilities are available. It accounts for the fact that competing causes reduce the opportunity for the selected cause to occur.1
How the calculation works
Convert each independent probability to a force, add the forces, calculate total survival, then allocate the total decrement probability to the selected cause in proportion to its force.2
qj = [μj / Σμk] × [1 − exp(−Σμk)], where μj = −ln(1 − q′j) 1Inputs and interpretation
Supply independent rates for the same population and year, each from zero inclusive to one exclusive, and choose the cause with a one-based index. If all rates are zero, the dependent rate is zero.
Limitations and assumptions
Constant forces within the year are essential to this conversion. Independent rates estimated on incompatible bases or periods cannot be safely combined, and other within-year assumptions lead to different results.
References
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Supplementary Notes for Actuarial Mathematics for Life Contingent Risks — Society of Actuaries
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Actuarial science — Wikipedia contributors
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