Cause-specific multiple-decrement probability from a table

Computes the probability of decrement from cause j within n years: $$ {}_nq_x^{(j)} = \sum_{k=0}^{n-1} {}_kp_x^{(\tau)}q_{x+k}^{(j)}. $$

Usage

nqxj_md(tbl, x, n, j)

Arguments

tbl

A multiple-decrement table produced by md_table().

x

Starting age or duration. May be scalar or vector.

n

Nonnegative integer term. May be scalar or vector.

j

Positive integer cause index. May be scalar or vector.

Value

A numeric vector of cause-specific decrement probabilities.

Examples

ages <- 45:50
qmat <- cbind(
  q1 = c(0.011, 0.012, 0.013, 0.014, 0.015, 0.016),
  q2 = rep(0.100, 6)
)
tbl <- md_table(ages, qmat, radix = 1000)

nqxj_md(tbl, x = 46, n = 2, j = 1)
#> [1] 0.023544