Loss Models, 5th Edition

3Basic Distributional Quantities

3.1 Moments

There are a variety of interesting calculations that can be done from the models described in Chapter 2. Examples are the average amount paid on a claim that is subject to a deductible or policy limit or the average remaining lifetime of a person age 40.

Definition 3.1

The kth raw moment of a random variable is the expected (average) value of the kth power of the variable, provided that it exists. It is denoted by or by . The first raw moment is called the mean of the random variable and is usually denoted by .

Note that is not related to , the force of mortality from Definition 2.7. For random variables that take on only nonnegative values (i.e. ), k may be any real number. When presenting formulas for calculating this quantity, a distinction between continuous and discrete variables needs to be made. Formulas will be presented for random ...