Computes the value of the log-likelihood function
$$L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \int_{x_1}^{x_m} \exp(\phi(t)) dt,$$
a new candidate for \(\phi\) via the Newton method as well as the directional derivative of \({\bold{\phi}} \to L({\bold{\phi}})\) into that direction.
Local_LL_all(x, w, phi)
Vector of independent and identically distributed numbers, with strictly increasing entries.
Optional vector of nonnegative weights corresponding to \({\bold{x}_m}\).
Some vector \({\bold{\phi}}\) of the same length as \({\bold{x}}\) and \({\bold{w}}\).
Value \(L(\phi)\) of the log-likelihood function at \(\phi.\)
New candidate for \(\phi\) via the Newton-method, using the complete Hessian matrix.
Directional derivative of \(\phi \to L(\phi)\) into the direction \(\phi_{new}.\)