Decide Whether Severe Claims Are Errors

Why a Severe Claim Needs Investigation

A very large claim can dominate a summary or strongly affect a model, so it deserves attention. But size alone does not establish that a record is wrong. A severe claim may be a legitimate consequence of a major loss, several payments on one claim, or coverage details that differ from those of ordinary claims. Conversely, a plausible-looking amount can still be wrong because of a unit conversion, transcription, or aggregation error.

The task is therefore not to make every claim look typical. It is to determine what the record represents, whether its recorded value is supported by evidence, and whether that value belongs in the analysis being conducted. A data decision should be tied to both the evidence and the prediction target.

Definition: A severe claim is a claim with an amount large relative to a specified reference, such as the other claims in the data or a fitted severity distribution. A severe claim is not necessarily an error. A data error is a recorded value or record that fails to represent the intended quantity accurately, as shown by evidence such as a verified unit mismatch, transcription mistake, or duplicate record.

The reference matters. A value may be extreme among routine claims but expected in a portfolio that includes catastrophe losses. Also state what the claim amount measures: paid amount to date, final paid amount, incurred amount, or another defined quantity. These values are not interchangeable. A large incurred amount may include a case reserve that is not yet paid; a large paid amount may reflect multiple valid installments.

A Disciplined Investigation

Use the following sequence before changing an extreme value. It keeps a statistical flag separate from a verified data correction and makes the final decision auditable.

Define the observation and target.
Identify whether one row represents a payment, a claim, a policy period, or another unit. Specify the claim measure and the prediction target.

Check the source and transformations.
Trace the amount to its source record. Verify currency, units, decimal placement, dates, and any aggregation or conversion applied during data preparation.

Check claim context.
Review the available claim status, coverage, limits, payment history, and event information. Ask whether the amount is consistent with the claim as recorded, without assuming that a rare event is impossible.

Assess statistical extremeness.
Use summaries, plots, or a suitable severity distribution to describe how unusual the amount is. Treat this as a reason to investigate, not as proof of an error.

Choose and document a treatment.
Correct a verified error; retain a supported valid claim; cap only when a defined analysis requires a cap; and exclude only when the record is outside the target population or cannot be used for a stated reason.

These steps distinguish four actions that are sometimes wrongly treated as equivalent. Correction replaces a value with a verified value. Retention keeps a valid observation, even if it is unusual. Capping replaces values above a stated threshold with that threshold for a specified analysis. Exclusion removes a record from that analysis. Capping and exclusion change the data used; neither should be described as correcting an error unless evidence shows the original record was wrong.

Statistical Rarity Is a Screening Signal

A distributional check can put an amount in context. For example, a fitted lognormal model may be useful for positive, right-skewed claim amounts. If $X$ is the claim amount and $\ln X\sim N(\mu,\sigma^2)$, then for $x>0$,

P(X>x)=1-\Phi\left(\frac{\ln x-\mu}{\sigma}\right),

where $\Phi$ is the standard normal cumulative distribution function. This is a model-based tail probability: it describes how often an amount above $x$ would occur under the assumed fitted distribution. It is not the probability that a particular record is erroneous. The calculation also depends on the population, period, coverage, and severity definition used to fit the distribution. A model fitted to routine claims may not represent a portfolio containing a different mix of risks or catastrophe claims.

A simple graphical check can be helpful as well. On a boxplot, a point beyond the whiskers is flagged by a conventional rule, not declared invalid. The flag identifies a value to examine. Source records and claim context determine whether there is evidence to alter it.

Derivation: Suppose $n$ claim amounts $x_1,\ldots,x_n$ have mean $\bar{x}=(\sum_{j=1}^{n}x_j)/n$. If one amount $x_k$ is replaced by $x_k'$, the new mean is $$ \bar{x}'=\frac{\sum_{j=1}^{n}x_j-x_k+x_k'}{n} =\bar{x}+\frac{x_k'-x_k}{n}. $$ Thus the mean changes by $(x_k'-x_k)/n$. This follows directly because all unchanged observations remain in the sum. The result explains why one severe claim can move a mean substantially, but it does not establish that the claim should be changed.

Worked Decisions

Worked Example: Correct a Verified Unit Error

Method and mistake avoided. Trace the amount to its source before changing it. The hypothetical data contain five claim amounts, recorded in thousands of dollars: $5, 7, 8, 9, 500$. A source-system check confirms that the final amount should be 50 thousand dollars; a decimal-placement error caused it to be recorded as 500 thousand dollars. Treat the five observations as an empirical distribution that assigns probability $1/5$ to each recorded claim; no parametric severity model is assumed. The task is to correct the verified error and quantify its effect on the mean.

Step 1: Calculate the recorded total and mean. In thousands of dollars, the total is $5+7+8+9+500=529$. The recorded mean is $529/5=105.8$ thousand dollars, equivalent to $105,800.

Step 2: Apply the source-verified correction. Replacing 500 by 50 gives the total $5+7+8+9+50=79$ thousand dollars. The corrected mean is $79/5=15.8$ thousand dollars, equivalent to $15,800.

Step 3: Check the effect. The value decreases by $500-50=450$ thousand dollars. With five observations, the mean decreases by $450/5=90$ thousand dollars. Directly, $105.8-15.8=90$ thousand dollars, so the calculation checks.

The median is 8 thousand dollars both before and after correction: the middle ordered value is 8 in each case. The correction is justified by the source record, not by the mean or by the fact that 500 is far from the other observations. A common mistake would be to write the arithmetic $529/5$ as $105,800 without first stating that the inputs are in thousands. The consistent statement is $529/5=105.8$ thousand dollars, equivalent to $105,800.

Worked Example: Retain a Rare but Supported Claim

Method and mistake avoided. Use a stated severity distribution to assess rarity, then check the record separately. In this hypothetical portfolio, claim amounts $X$ are measured in thousands of dollars. Assume the fitted model is $\ln X\sim N(\ln 20,(\ln 2)^2)$. Thus the log-scale mean parameter is $\ln 20$, the log-scale standard deviation is $\ln 2$, the median claim is 20 thousand dollars, and the geometric standard deviation is 2. A claim is recorded at 90 thousand dollars. Source documentation and claim details confirm that it is a valid covered claim.

Step 1: Standardize the observed amount. Under the model, $$ z=\frac{\ln(90)-\ln(20)}{\ln 2} =\frac{\ln(90/20)}{\ln 2} =\frac{\ln(4.5)}{\ln 2} \approx\frac{1.5041}{0.6931} \approx 2.1699. $$

Step 2: Calculate the model tail probability. The probability of a claim exceeding 90 thousand dollars is approximately $1-\Phi(2.1699)=0.0150$, or 1.50%. As a check on the scale of this result, a claim of 80 thousand dollars has $z=\ln(80/20)/\ln 2=\ln(4)/\ln 2=2$, giving $P(X>80)=1-\Phi(2)\approx0.0228$. Since 90 is greater than 80, its model tail probability should be smaller than 0.0228; 0.0150 is consistent.

Step 3: Decide what the calculation establishes. The model says that amounts above 90 thousand dollars are uncommon under the stated assumptions. It does not say that the observed amount is an error. Here, the source and claim details support the value, so retain 90 thousand dollars for an analysis whose target includes such claims. Document the distributional check and the source verification.

The common mistake is to label a claim erroneous solely because its tail probability is small. A tail probability describes rarity under a model; it does not validate the model for every kind of claim or replace a source check.

Worked Example: Preserve Payment History When Building Claim-Level Data

Method and mistake avoided. Reconcile payment records to the intended observation unit before deciding whether a large total is a duplicate. A hypothetical claim-level severity table should contain one total per claim. Four claim totals are 12, 15, 18, and 20 thousand dollars, and a fifth claim has two documented installments of 210 thousand dollars each. Assume the intended empirical distribution gives equal weight to each of the five claims; no parametric severity model is assumed. The source confirms that the two installments are separate payments on one valid claim.

Step 1: Construct the claim-level amount. The fifth claim total is $210+210=420$ thousand dollars. The claim-level data are therefore $12, 15, 18, 20, 420$ thousand dollars.

Step 2: Calculate the claim-level mean. The first four amounts sum to $12+15+18+20=65$ thousand dollars. Including the fifth claim gives $65+420=485$ thousand dollars, so the mean is $485/5=97$ thousand dollars.

Step 3: Show the consequence of treating an installment as a duplicate. If one valid 210-thousand-dollar installment were incorrectly dropped, the fifth claim would be recorded as 210 thousand dollars. The resulting total would be $65+210=275$ thousand dollars and the mean would be $275/5=55$ thousand dollars. The mean would be understated by $97-55=42$ thousand dollars.

Step 4: Check the observation unit. The correct claim-level table has five observations. Keeping the two installments as separate rows would instead create six payment rows and answer a payment-level question, not the intended equal-weight-per-claim question. The correct treatment is to aggregate the documented installments for the claim and retain the resulting 420-thousand-dollar amount.

The common mistake is to remove one of two similar-looking payment records without checking whether they are duplicate records or distinct installments. Similar amounts are not proof of duplication. Here, the source records establish that both payments belong in the claim total.

Choosing a Treatment for the Analysis

A valid amount can still require careful handling, but the action should reflect the analysis objective. For predicting total claim cost, removing a legitimate severe claim can systematically understate the target. For an analysis explicitly restricted to routine claims, a valid catastrophe claim may be outside the target population, but that restriction must be defined and reported rather than disguised as data cleaning. The same portfolio can support different analyses with different inclusion rules.

Evidence and purpose	Defensible treatment	What to document
A source record verifies a transcription, unit, or conversion error.	Correct the value to the verified amount.	The original value, verified value, source, and correction rule.
The amount is unusual but source and claim checks support it.	Retain it if it belongs to the target population.	The validation performed and why the claim is in scope.
The analysis has a defined operational or scientific cap.	Apply the cap only for that analysis; preserve the uncapped amount.	The threshold, reason for capping, and results with the original amount where relevant.
The record is outside the defined target population or is unusable for a stated reason.	Exclude it from that analysis, not silently from the underlying data.	The exclusion criterion, number of affected records, and implications.

A cap changes the quantity being analyzed. If $X$ is the original amount and the chosen cap is $c$, the capped value is $\min(X,c)$. The average of capped amounts is generally not the average of original amounts: every observation above $c$ contributes $c$ rather than its actual amount. A cap can be useful for a specified robustness analysis, but it should not be presented as the true claim amount.

When a decision is uncertain, preserve the raw value and create a separate analysis field or a documented inclusion flag. Compare conclusions under defensible alternatives when the choice could materially affect results. In a predictive setting, the treatment must also respect how the target is defined: correcting a verified recording error is different from changing valid outcomes to make them less influential. This discipline is aligned with the SOA Exam PA (Predictive Analytics) syllabus.

Common Mistakes

Calling an outlier an error. A boxplot flag or small tail probability indicates unusualness, not invalidity.
Changing a value because it moves the mean. Statistical influence is a reason to investigate; it is not evidence supporting a correction.
Confusing payments with claims. Multiple valid payments can belong to one claim. Determine the intended row unit before removing or aggregating records.
Capping without defining the purpose. A cap changes the analyzed quantity and can understate valid severe losses.
Failing to preserve the audit trail. Keep the original amount, the action taken, and the evidence for that action.

Key takeaway: Investigate an extreme claim by combining source checks, claim context, and statistical evidence. Correct only a verified error; retain valid in-scope claims; and make any cap or exclusion explicit, purpose-specific, and documented.

Check Your Understanding

For each hypothetical case, choose the defensible treatment and check the calculation where requested.

A claim table in thousands of dollars contains $4, 6, 7, 8, 300$. A source audit confirms the last value should be 30 because of a misplaced decimal. What are the recorded and corrected means, in thousands of dollars? (Answer: $325/5=65$ thousand dollars recorded; $55/5=11$ thousand dollars corrected.)
A hypothetical fitted severity model is $\ln X\sim N(\ln 10,(\ln 2)^2)$, with $X$ in thousands of dollars. A supported claim is 40 thousand dollars. What is its model tail probability, approximately, and does that alone justify changing it? (Answer: $z=\ln(40/10)/\ln2=2$, so $P(X>40)\approx0.0228$; no, rarity alone does not justify changing a supported claim.)
A claim-level dataset has amounts 10, 12, and 18 thousand dollars, plus two payment rows of 60 thousand dollars each for one additional claim. What is the mean across the four claim totals after aggregation? (Answer: $(10+12+18+120)/4=40$ thousand dollars.)
A validated claim amount is 250 thousand dollars. An analysis of routine claims defines its target population to exclude documented catastrophe claims, and this claim is confirmed to be a catastrophe claim. What action is appropriate for that analysis, and what should happen to the original record? (Answer: Exclude it from that explicitly defined routine-claim analysis, document the reason, and preserve the original record.)
A valid in-scope claim dataset contains amounts 20, 30, and 200 thousand dollars. An analyst proposes a 100-thousand-dollar cap. What are the original and capped means, and what must the capped result be called? (Answer: Original mean $250/3\approx83.33$ thousand dollars; capped mean $(20+30+100)/3=50$ thousand dollars; describe it as a capped analysis, not as corrected claim severity.)

What You'll Learn