Estimation, Evaluation, and Selection of Actuarial Models

4.4. GRAPHICAL COMPARISON OF THE DENSITY AND DISTRIBUTION FUNCTIONS69
Exponential Fit
F(x)
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Model
Empirical
Model vs. data cdf plot for Data Set B censored at 1,000
Once again, the exponential model does not fit well.
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Exercise 75 Repeat the above example, using a Weibull model in place of the exponential model.
When the model’s distribution function is close to the empirical distribution function, it is
difficult to make small distinctions. Among the many ways to amplify those distinctions, two
will be presented here. The first is to simply plot the difference of the two functions. That is,
if F n (x) is the empirical distribution function and F ∗ (x) is the model distribution function, plot
D(x) =F n (x) − F ∗ (x).
Example 4.12 Plot D(x) for the previous example.
For Data Set B truncated at 50, the plot is as follows.