6. Calibration method The following three steps are taken separately for the two sexes : We take the exposures , and with and observed deaths for the relevant Western European countries, with and . This concerns in all cases the sum of all exposures and the sum of all deaths in the respective countries, including the Netherlands. The parameters were then determined in such a way that the Poisson likelihood function for the observed deaths is as large as possible for the given exposures: requiring the sum of the elements of elements of . To obtain a unique specification of the three vectors we normalise by over to be equal to and the sum of the over to be equal to . Data after 2014 are not available for all the relevant countries. For this reason, the values of then applied en , by means of with The maximum likelihood method is now applied to the data for the Netherlands to determine as previously. Once again, normalisation takes place by requiring the sum of the elements in over and In a fourth and final step, the four time series are used, namely , (now including the year 2015) and over to be respectively and . the parameters and matrix . On the assumption that the variables are independently and identically distributed and have a four-dimensional normal distribution with average (0,0,0,0) and covariance matrix , we select the estimators for and in such a way6 that the likelihood of these time series is maximised. 7. Simulation of the time series In order to be able to simulate the scenarios for the timeseries to estimate in the previous step are determined up to and including 2014. Linear extrapolation is , samples from a normal distribution with an average of (0,0,0,0) and covariance matrix C must be generated. This can be done by multiplying a (row) vector with four independently standard normally distributed variables by a matrix H, which satisfies the condition , in other words by means of . In the list of parameters in the publication and the accompanying Excel spreadsheet, a Cholesky H matrix has therefore also been included in addition to the covariance matrix C. 6 The working group made use of the R package, systemfit, for this with the options method=”SUR” and methodResidCov=”noDfCor”. Projection Table AG2016 Appendix A 35
36 Online Touch Home