Total-decrement lifetable from a multiple decrement table: lt_tau

Builds a single-decrement lifetable for the *total* decrement (any cause), using \(q_x^{(\tau)}\) from a multiple decrement table produced by md_table. This enables direct re-use of single-life functions (e.g., t_px, t_qx, t_Ex, annuities, insurances) under the total decrement model.

Usage

lt_tau(md, ...)

Arguments

md

A multiple decrement table (typically the output of md_table), containing columns x and q_total.

...

Additional arguments passed to lifetable (e.g., radix, omega, close, ax, type, frac, check, tol).

Value

A lifetable object as produced by lifetable.

Details

Given cause-specific decrement probabilities \(q_x^{(j)}\), the total decrement is \(q_x^{(\tau)} = \sum_j q_x^{(j)}\). This function simply passes x = md$x and qx = md$q_total to lifetable.

Examples

qx_df <- tibble::tibble(
  x = 30:35,
  q_death = c(0.001, 0.0012, 0.0014, 0.0017, 0.0020, 1.0000),
  q_disability = c(0.002, 0.0021, 0.0022, 0.0023, 0.0024, 0.0000)
)
md <- md_table(qx_df, radix = 1e5, close = TRUE)
lt <- lt_tau(md, radix = 1e5, close = TRUE, frac = "UDD")
t_px(lt, x = 30, t = 5)
#> [1] 0.9818329