Estimation, Evaluation, and Selection of Actuarial Models

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8 CHAPTER 2. MODEL ESTIMATION <strong>and</strong> then H(x) = Z x −∞ h(y)dy. The distribution function can be obtained from F (x) =1−S(x) =1−e −H(x) .Therefore,estimating the cumulative hazard function provides an alternative way to estimate the distribution function. In order to define empirical estimates, some additional notation is needed. For a sample <strong>of</strong> size n, lety 1
2.2. ESTIMATION USING DATA-DEPENDENT DISTRIBUTIONS 9 Example 2.10 Determine the empirical cumulative hazard rate function for the previous example. For the empirical cumulative hazard rate function, ⎧ 0, x < 1.0 ⎪⎨ Ĥ(x) = 1 8 =0.125, 1.0 ≤ x
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Estimation, Evaluation, and Selection of Actuarial Models

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