Motor insurance claims

One policy year of 1 500 private motor policies from a fictional insurer, Sahil Mutual Insurance. Each row is one policy: region, driver age band, vehicle value, the fraction of the year insured (exposure), the number of claims and the total amount claimed. Claim counts are over-dispersed relative to a Poisson model and claim amounts are heavily right-skewed with one very large claim — the core ideas of actuarial frequency–severity analysis.

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Rows: 1,500
Columns: 7
One row is: one motor policy (one policy year)
Version: v1

Data dictionary

Column	Type	Unit	Summary	Description
`policy_id` Policy	id			Policy number.
`region` Region	category		4 levels: Central, Eastern, Western, Southern	Region where the vehicle is registered.
`driver_age_band` Driver age band	ordinal		5 levels: 18-25, 26-35, 36-50, 51-65, 66+	Age band of the main driver.
`vehicle_value_sar` Vehicle value	number	SAR	mean 95500, median 83500, SD 52720, range 16500–551,500	Insured value of the vehicle.
`exposure_years` Exposure	number	years	mean 0.8892, median 1, SD 0.2343, range 0.1–1	Fraction of the year the policy was in force.
`claim_count` Claims	integer	claims	mean 0.1233, median 0, SD 0.4036, range 0–4	Number of claims during the period.
`total_claims_sar` Total claimed	number	SAR	mean 1463, median 0, SD 13520, range 0–480,000	Sum of claim amounts (0 for policies with no claims).

What it is good for

Compare the mean and variance of claim counts and recognise overdispersion.
Fit Poisson and negative-binomial style models with exposure and compare them.
Describe a heavy-tailed severity distribution (claimants only) with logs, percentiles and the effect of one extreme value on the mean.
Compute claim frequency and pure premium by driver age band.

Methods: Poisson distribution, dispersion index, negative binomial, Poisson regression with offset, log-normal distribution, skewness, percentiles.

Data quality notes

Most policies (about 90%) have no claim, so total_claims_sar is mostly 0: analyse severity on claimants only.
claim_count variance exceeds its mean (overdispersion).
One claim of 480 000 SAR dominates the total — check how the mean changes without it.
Partial-year policies have smaller exposure; compare rates per policy-year, not raw counts.
No missing values.

Provenance and licence

Exposure is 1 for 75% of policies and uniform 0.1–1 otherwise. Expected claim frequency = 0.12 per year × driver-age factor (18–25: 2.2, 26–35: 1.2, 36–50: 0.9, 51–65: 0.85, 66+: 1.1) × region factor × exposure. Claim count ~ negative binomial (gamma–Poisson, size 0.6), so policies vary in underlying riskiness beyond what the columns explain. Each claim's amount is log-normal (median ≈5 500 SAR, sd 1.1 on the log scale), rising slightly with vehicle value; total_claims_sar is the sum. One policy has a single claim of 480 000 SAR.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241028). It does not describe real people or organisations; any resemblance is coincidental.

Preview

Dataset

Motor insurance claims

1,500 rows · one row = one motor policy (one policy year) · synthetic data

About this dataset Open in the lab

Policy	Region	Driver age band	Vehicle value (SAR)	Exposure (years)	Claims (claims)	Total claimed (SAR)
POL0001	Central	36-50	168500	1	0	0
POL0002	Eastern	51-65	27500	1	0	0
POL0003	Western	26-35	106500	1	0	0
POL0004	Eastern	26-35	152000	0.94	0	0
POL0005	Western	26-35	101000	1	2	8429.6
POL0006	Eastern	51-65	72000	0.98	0	0
POL0007	Southern	18-25	83500	1	0	0
POL0008	Central	36-50	48000	1	0	0
POL0009	Central	26-35	73000	1	0	0
POL0010	Southern	36-50	108500	0.59	0	0
POL0011	Eastern	66+	147500	1	0	0
POL0012	Eastern	51-65	69500	1	0	0

Used in

Shape: skewness and kurtosis · Describing Data
Probability rules · Probability
Expected value and variance of a random payoff · Probability
Random variables and their distributions · Probability Distributions
The Poisson distribution · Probability Distributions
Choosing and checking a distribution · Probability Distributions
The law of large numbers · Sampling and the Central Limit Theorem
The central limit theorem · Sampling and the Central Limit Theorem
Bootstrap intervals · Estimation and Confidence Intervals
Monte Carlo simulation · Resampling and Statistical Reasoning
Robust statistics · Resampling and Statistical Reasoning
Reproducibility and ethics · Resampling and Statistical Reasoning
Pricing for rare large claims · Case