Appendix D
Accelerated Lifetime Model
(Source: Franses and Paap [1])
In the estimation of duration models, the log-likelihood function is
(D.1) 
where 
is defined as a 0/1 dummy that is 1 if the observation is not censored and 0 if the observation is censored, and 
is a vector of the model parameters consisting of 
and the distribution-specific parameters. The log-likelihood function is given by
(D.2) 
The maximum likelihood (ML) estimator 
is the solution of the equation
(D.3) 
In general, there are no closed-form expressions for this estimator and we have to use numerical optimization algorithms such as Newton–Raphson to maximize the log-likelihood function. The ML estimates can be found by iterating over
until convergence, where and denote the first- and second-order derivatives ...
