Unlike its connotation in statistics, frequency, as used here, is not a count nor is it necessarily a probability estimate, as would be a “relative frequency” in statistical usage. To illustrate this latter statement, in the foregoing example, the exposure might have been measured in units of 100 car-years; again, in case of air travel insurance, exposure might be in terms of 1000 passenger-hours. One notes, however, that frequency is an estimate of the expected number of insured events per exposure unit. Sometimes, when the meaning is clear, the word frequency is used for that expected value itself.
Although frequency is not the principal topic of this text, it is obviously an extremely important measure in placing a value on an insurance contract. It should also be noted that the terms of the insurance contract itself have a determining effect on frequency. For example, if Automobile Collision Insurance excludes payment for the first $250 of any loss, then there will be no payment at all for losses under $250 and hence the number of occurrences of insured events is reduced. Alternatively, if Accident and Sickness Insurance excludes disability for periods of seven days or less, then there will be no payment for periods of disability fewer than eight days and hence the number of reported cases is smaller.
Most important, for the purpose of this text, is the question “If the insured event occurs, what will be the cost to the insurer?” This cost (or loss) is, of course, a random variable. One characteristic of several such costs, arising from the occurrence of similar insured events, is the mean value, sometimes referred to as a mean severity, or, to conform with
business usage, simply severity. That is, severity is the ratio