b_3(t) = g'(g^{-1}(t))^2 f_X(t) - g''(g^{-1}(t)) S_X(t), the
coefficient carried by the SECOND cumulative survival estimator.
Note the minus sign and the survival function: this is where the
two Ch. 4 estimators part company.
Usage
morie_fauzi_b3_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_3, g_prime, g_double_prime, bias_order,
contrast, transform, method.
References
Fauzi and Maesono (2023), Eq. (4.21).
Examples
morie_fauzi_b3_coefficient(1, f_X = 0.5, S_X = 0.4)$b_3
#> [1] 0.1
