It is also common to display multi-decrement tables using a “life table” format. With the expected number of lives given by each status. To this end, let
- (x_0) be an initial age
- (l_{x_0}) be the expected number in state 0 (.e.g., “alive”) at age (x_0); this is the radix of the table
- (l_x) be the expected number in state 0 at age (x); this is computed as (l_x = l_{x_0} times ~_{x-x_0} p_{x_0})
- ( d_x^{(j)}) number of transitions from state 0 to state (j) (i.e., exits due to cause (j)), from ages (x) to (x+1).
Here is an example of a quadruple decrement table where
- (j=0) means an active policyholder of a life insurance policy,
- (j=1) corresponds to death,
- (j=2) surrender of a life insurance policy, and
- (j=3) diagnosis of a critical illness.