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Contingent multi-life probabilities

multilife_contingent_probabilities.Rd

Computes probabilities associated with the order of death of two independent lives over a specified term.

Usage

tqxy1(x, y, n, tbl = NULL, model = NULL, ...)

tqyx1(x, y, n, tbl = NULL, model = NULL, ...)

tqxy2(x, y, n, tbl = NULL, model = NULL, ...)

tqyx2(x, y, n, 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.

n

Term in years. May be scalar or vector.

tbl

Optional life table object retained for backward compatibility. Continuous calculations currently require model.

model

Parametric survival model.

...

Additional parameters passed to the survival and hazard functions.

Value

A numeric vector of contingent probabilities.

Details

tqxy1() computes the probability that the first life dies before the second life within \(n\) years.

tqyx1() computes the probability that the second life dies before the first life within \(n\) years.

tqxy2() computes the probability that the first life dies after the second life but within \(n\) years.

tqyx2() computes the probability that the second life dies after the first life but within \(n\) years.

These functions require a parametric survival model because an annual life table does not uniquely determine the within-year order of death without an additional interpolation assumption.

All calculations assume the two future lifetimes are independent.

The probabilities are obtained by integrating the joint survival function together with the appropriate force of mortality.

The four functions partition the probability that one of the two lives dies within the specified term according to the order of death.

Examples

tqxy1(
  40, 50,
  n = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.15

tqyx1(
  40, 50,
  n = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.1833333

tqxy2(
  40, 50,
  n = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.01666667

tqyx2(
  40, 50,
  n = 10,
  model = "uniform",
  omega = 100
)
#> [1] 0.01666667