fun_F <- function(est, t, inputX) {
lambda <- exp(est[1])
phi <- exp(est[2])
rho <- exp(est[3])
b <- est[-c(1:3)]
bX <- sum(b * inputX)
1 - (1 + rho * (t/lambda)^phi * exp(bX))^(-1/rho)
}
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