Information Matrix

In 1860 William Makeham published a famous paper. In it he extended Gompertz's mortality law to include a constant term:

\[\mu_x=e^\epsilon+e^{\alpha+\beta x}\qquad(1),\]

The foundation for most modern statistical inference is the log-likelihood function.  By maximising the value of this function, we find the maximum-likelihood estimate (MLE) for a given parameter, i.e. the most likely value given the model and data.  For models with more than one parameter, we find the set of values which jointly maximise the log-likelihood.