Schuette-Nesbitt formula

In mathematics, the Schuette–Nesbitt formula is a generalization of the inclusion–exclusion principle. It is named after Donald R. Schuette and Cecil J. Nesbitt.

The probabilistic version of the Schuette–Nesbitt formula has practical applications in actuarial science, where it is used to calculate the net single premium for life annuities and life insurances based on the general symmetric status.

Consider a set Ω and subsets A₁, ..., A_m. Let

${\displaystyle N(\omega )=\sum _{n=1}^{m}1_{A_{n}}(\omega ),\qquad \omega \in \Omega ,}$

 

 

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