Claim-Level Severity Targets and Sampling Units

What a Claim Severity Model Measures

A severity model describes the amount associated with an individual claim, not the number of claims generated by a policy. Its response is therefore defined on a claim-level observation. This choice sounds simple, but a policy can produce no claims, one claim, or several claims; those alternatives affect which records enter the severity data and how an average should be calculated.

The target also depends on which claims the data include. A model fitted to claims that were reported under a particular reporting process describes those claims, subject to the model’s predictors and assumptions. It does not automatically describe every loss that could have occurred, every unreported event, or every claim under a different coverage or reporting rule.

The amount basis and inclusion rule should be stated before fitting or interpreting a model. For example, paid loss and incurred loss are not interchangeable responses. Nor are reported claims necessarily the same population as all events that occurred: events may be reported late, omitted from a data extract, or subject to a stated eligibility rule. The severity target is conditional on the population actually represented in the observations.

If a claim-level model uses policy characteristics such as territory or vehicle class, those characteristics may be copied onto each claim row for the relevant policy. That does not turn the rows into policy observations: each row still represents a claim. Policies with more claims consequently contribute more claim observations to a claim-level average.

Claim Weighting and Policy Weighting

Suppose policy \(i\) has \(n_i\) included claims, with observed severities \(Y_{i1},\ldots,Y_{in_i}\). Let \(\bar Y_i\) be the mean severity for that policy when \(n_i>0\), and let \(N=\sum_i n_i\) be the total number of included claims. When the target is the average amount per included claim, each claim receives equal weight.

By contrast, an average of policy means gives each policy with at least one claim equal weight, regardless of its claim count. These are different summaries unless the policies have equal claim counts or their claim means happen to produce the same result. A policy with no included claims has no policy-specific claim mean; it must not be assigned a severity of zero merely to make a policy-level average possible.

Why the Claim-Level Formula Has Claim Counts in It

The claim-level average can be rewritten in terms of policy means, but a policy’s claim count must then act as its weight. To see why, for each policy with claims, the total severity is \(n_i\bar Y_i\). Summing those totals across policies gives the total across all claim rows. Dividing by the total number of claim rows gives the claim-level average:

Thus the claim-level mean is a weighted average of policy means, with weights proportional to each policy’s number of included claims. This is also the natural finite-data answer to the question, “What is the average recorded severity if one claim is selected uniformly from the included claim records?” Each claim has the same chance of being selected; a policy with more claims therefore has more chances to supply the selected claim.

If claims are sampled from a broader process rather than enumerated completely, interpreting the sample mean as an estimate of a population mean additionally requires the sample to represent the target claim population. Multiple claims from one policy can also be related. That relationship matters when assessing uncertainty, but it does not change which record is the claim-level observation.

Policy Records Are Not Automatically Severity Observations

A policy file often contains one row per policy, with a claim count and perhaps a total loss amount. Such a file can be useful for many analyses, but it is not the same as a claim-level severity file. A policy total combines all claims for that policy; a claim count tells how many claims contributed to that total but does not reveal their individual severities. To calculate a claim-level mean from policy summaries, total claim severity and total claim count are sufficient. To model individual claim responses, the separate claim records and their associated predictors are generally needed.

Selection Rules Define the Population Represented

The phrase “claim severity” is incomplete unless the included-claim population is clear. A data set may include only claims reported during a specified period, claims from selected coverages, or records meeting another explicit inclusion rule. A model fitted to those observations describes severities conditional on that rule. If the probability of inclusion varies with severity or with a predictor, the included claims may have a different severity distribution from the broader set of losses.

For example, if a hypothetical reporting process captures only events with recorded amounts at or above a stated threshold, its observed severity sample omits amounts below that threshold. The arithmetic mean of the recorded claims is still well-defined, but it answers a conditional question about captured claims—not the mean amount of all events. Recognizing that distinction is essential before interpreting a fitted model or applying it to a different population. The appropriate treatment of specific deductibles, limits, or censoring mechanisms depends on how the response is recorded and is a separate modeling question.

Exam Checks Before Fitting a Severity Model

Before interpreting a severity response, make the observation unit, amount basis, and inclusion rule explicit. Then check that the calculation’s numerator and denominator refer to the same records. A claim total divided by a policy count is not a claim-level average, and a policy with no claims is not a claim with zero severity.

The distinction also matters when severity records are built from policy data. Repeating a policy’s characteristics on each of its claim rows is consistent with a claim-level model, but it means policies with more claims contribute more rows. Conversely, aggregating all claims into one policy total changes the response and observation unit; it should not be treated as a harmless formatting change.