Multi-life survival and failure probabilities

Computes joint-life and last-survivor survival and failure probabilities for two independent lives.

Usage

tpxy(x, y, t, tbl = NULL, model = NULL, ...)

tqxy(x, y, t, tbl = NULL, model = NULL, ...)

tpxybar(x, y, t, tbl = NULL, model = NULL, ...)

tqxybar(x, y, t, tbl = NULL, model = NULL, ...)

Arguments

x

Age of the first life. May be scalar or vector.

y

Age of the second life. May be scalar or vector.

t

Nonnegative duration. May be scalar or vector.

tbl

Optional life table object.

model

Optional parametric survival model.

...

Additional parameters passed to the survival model.

Value

A numeric vector of probabilities.

Details

tpxy() computes the joint-life survival probability $$ {}_tp_{xy} = {}_tp_x\,{}_tp_y. $$

tqxy() computes the joint-life failure probability $$ {}_tq_{xy} = 1-{}_tp_{xy}. $$

tpxybar() computes the last-survivor survival probability $$ {}_tp_{\overline{xy}} = {}_tp_x + {}_tp_y - {}_tp_x\,{}_tp_y. $$

tqxybar() computes the last-survivor failure probability $$ {}_tq_{\overline{xy}} = 1-{}_tp_{\overline{xy}}. $$

All calculations assume the future lifetimes are independent.

Joint-life probabilities require both lives to satisfy the survival condition, whereas last-survivor probabilities require at least one life to survive.

Examples

tpxy(
  40, 50,
  t = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.6666667

tqxy(
  40, 50,
  t = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.3333333

tpxybar(
  40, 50,
  t = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.9666667

tqxybar(
  40, 50,
  t = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.03333333