b_2(t) = g'(g^{-1}(t))^2 f_X(t) + int_{g^{-1}(t)}^Inf g''(z) g'(z) f_X(g(z)) dz.
The tail integral is taken by quadrature on the transformed scale,
where the integrand is smooth. b_2 is the coefficient carried by
the FIRST cumulative survival estimator.
Usage
morie_fauzi_b2_coefficient(
t,
f_X,
f_X_prime = NULL,
S_X = NULL,
transform = "log"
)
Arguments
- t
evaluation points strictly inside the support.
- f_X
density at t.
- f_X_prime
density derivative at t; required here.
- S_X
survival at t; unused by b_1, kept for signature
parity with the b_2 and b_3 companions.
- transform
"log" or "identity".
Value
list: t, b_2, g_prime, g_double_prime, bias_order,
contrast, transform, method.
References
Fauzi and Maesono (2023), Eq. (4.15).
Examples
morie_fauzi_b2_coefficient(c(1, 2), f_X = c(0.4, 0.1))$b_2
#> [1] 0.7553231 0.4060150
