Estimation, Evaluation, and Selection of Actuarial Models

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16 CHAPTER 2. MODEL ESTIMATION 8. Calculate the first S(y) value. For this example, cell J16 becomes = (H16 − I16)/H16. 9. The remaining values of the survival function can be calculated in column J. For cell J17, the formula is = J16*(H17 − I17)/H17 which can be copied into the remaining cells. Example 2.17 Determine the Kaplan-Meier estimate for Data Set D2. Based on the previous example, we have ⎧ 1, 0 ≤ t
2.2. ESTIMATION USING DATA-DEPENDENT DISTRIBUTIONS 17 Integrating both sides yields Z t Z ds(u) t 0 r(u) = h(t)dt = H(t). 0 Now replace the true expected count s(t) by ŝ(t), the observed number of deaths by time t. Itisa step function, increasing by s i at each death time. Therefore, the left-hand side becomes X s i r i which defines the estimator, Ĥ(t). The Nelson-Åalen estimator is ⎧ ⎪⎨ 0, 0 ≤ t
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Estimation, Evaluation, and Selection of Actuarial Models

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