Lhat_eta: Value of the Log-Likelihood Function L, where Input is in Eta-Parametrization
Description
Gives the value of
$$L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \int_{x_1}^{x_m} \exp(\phi(t)) dt$$
where $\phi$ is parametrized via
$${\bold{\eta}}({\bold{\phi}}) = \Bigl(\phi_1, \Bigl(\eta_1 + \sum_{j=2}^i (x_i-x_{i-1})\eta_i\Bigr)_{i=2}^m\Bigr).$$
Usage
Lhat_eta(x, w, eta)
Arguments
x
Vector of independent and identically distributed numbers, with strictly increasing entries.
w
Optional vector of nonnegative weights corresponding to ${\bold{x}_m}$.
eta
Some vector ${\bold{\eta}}$ of the same length as ${\bold{x}}$ and ${\bold{w}}$.
Value
Value $L({\bold{\phi}}) = L({\bold{\phi}}({\bold{\eta}}))$ of the log-likelihood function is returned.