On the use of limited-value averages in actuarial modelling

In actuarial modelling, certain statistical tests, such as Pearson's chi-square test, are commonly used for evaluating the goodness of fit. Besides these standard tests, occasionally the limited-value averages (LVAs) are also examined for such purposes and are compared, in a rather casual manner, with the corresponding limited-value expectations under the specified distribution law. In fact, as there are often coverage limits in practice, the LVAs are probably more relevant to the dollar values involved in the losses. In this article, we explore the application of a formal statistical setting of the LVAs test for goodness-of-fit testing. We apply it to the well-known hurricane loss data and also another set of individual claims data. Two simulation experiments are carried out to study the limiting chi-square property and the power of the test. A formal proof of the limiting property is provided in the appendix. Our results suggest that this LVAs test is potentially suitable for wider use in actuarial practice.