Normal behaviour

One interesting aspect of maximum-likelihood estimation is the common behaviour of estimators, regardless of the nature of the data and model.  Recall that the maximum-likelihood estimate, \(\hat\theta\), is the value of a parameter \(\theta\) that maximises the likelihood function, \(L(\theta)\), or the log-likelihood function, \(\ell(\theta)=\log L(\theta)\).  By way of example, consider the following three single-parameter distributions:

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Spotting hidden data-quality issues

The growing market for longevity risk-transfer means that takers of the risk are keenly interested in the mortality characteristics of the portfolio concerned. The first thing requested by the risk-taker is therefore detailed data on the portfolio's recent mortality experience.  This is ideally data extracted on a policy-by-policy basis.

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