Skip to contents

Theorem 4.6: the mean-residual-life identity at the start of support

Source: R/fauzi_native.R
morie_fauzi_theorem_4_6.Rd

(4.29): m~(a_1) + a_1 = Xbar + O_p(h^2). At the left end of the support nobody has failed yet, so the expected remaining lifetime is the expected lifetime. A large gap is a diagnostic: a bandwidth too big, or a transformation mismatched to the support.

Usage

morie_fauzi_theorem_4_6(x, a1, mrl_at_a1, h = NULL)

Arguments

x

numeric sample.

a1

the lower bound of the support.

mrl_at_a1

the estimated MRL at a1.

h

bandwidth, to set the O(h^2) tolerance; optional.

Value

list: identity_lhs, sample_mean, gap, expected_order, within_expected, a1, n, why_it_holds, diagnostic_use, method.

References

Fauzi and Maesono (2023), Theorem 4.6, Eq. (4.29).

Examples

set.seed(1)
if (requireNamespace("ranger", quietly = TRUE)) {
  x <- stats::rexp(200)
  morie_fauzi_theorem_4_6(x, 0, mean(x))$gap
}
#> [1] 0