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logcondens (version 2.1.8)

Local_LL_all: Log-likelihood, New Candidate and Directional Derivative for L

Description

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.

Usage

Local_LL_all(x, w, phi)

Value

ll

Value \(L(\phi)\) of the log-likelihood function at \(\phi.\)

phi_new

New candidate for \(\phi\) via the Newton-method, using the complete Hessian matrix.

dirderiv

Directional derivative of \(\phi \to L(\phi)\) into the direction \(\phi_{new}.\)

Arguments

x

Vector of independent and identically distributed numbers, with strictly increasing entries.

w

Optional vector of nonnegative weights corresponding to \({\bold{x}_m}\).

phi

Some vector \({\bold{\phi}}\) of the same length as \({\bold{x}}\) and \({\bold{w}}\).