3. Closure of the table For ages above 90 years, with , the Kannistö closure method is used, which is based on a logical regression using the table for ages . The number of ages on which the regression is based is therefore , the average of these ages is and the sum of the squares of the deviation is Closure using the Kannistö technique means that for . . where and are respectively the logical and inverse logical functions. and the regression weights are given by If a mortality probability is required for an age greater than 120, it is assumed to be equal to the mortality probability for the age of 120. 4. Best estimates for mortality probabilities and life expectancy Since we identify the best estimates for future values of the time series with the most likely outcomes, these correspond to the series for and , which are obtained by filling in for all values of . The covariance matrix is therefore not required to generate these best estimates, but is necessary to carry out simulations which may help in analysing uncertainty in relation to the best estimates. under the assumption that this person was born on 1 January of year (with and ) and assume that someone who dies within a calendar year on average is still alive during the calendar year for six months, we find for this so-called cohort life expectancy: Note that according to this The probability that the person at time is still alive is, after all, the product of mortality probabilities for all years s between and , whereby every year the person not only ages by a year older, but we also have to take into account on each occasion a new column in the mortality table. This last effect is not included in the period life expectancy: which suggests that the mortality probabilities of today (time ) will no longer change over time. This results in an incorrect impression of life expectancy and although this period life expectancy is often , this is incorrect. Projection Table AG2016 Appendix A 33
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