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📊 '''Severity distribution''' is a statistical model that describes the probability of different loss amounts — how large individual [[Definition:Claim | claims]] are likely to be — within an insurance portfolio. While [[Definition:Frequency distribution | frequency distribution]] addresses how often losses occur, severity distribution focuses on the magnitude of each loss event, making the two complementary building blocks of virtually every [[Definition:Actuarial science | actuarial]] pricing and reserving exercise. Common distributional forms used in insurance include the lognormal, Pareto, Weibull, and gamma distributions, each chosen for its ability to fit observed claims data in particular lines of business — heavy-tailed distributions like the Pareto, for example, are often applied to [[Definition:Catastrophe risk | catastrophe]] and [[Definition:Liability insurance | liability]] lines where extreme losses, though rare, dominate total portfolio cost.

⚙️ Fitting a severity distribution to empirical data typically involves collecting historical [[Definition:Loss | loss]] amounts, adjusting them for inflation and [[Definition:Loss development | development]], and then using statistical techniques such as maximum likelihood estimation or method-of-moments to parameterize a candidate distribution. Actuaries test the goodness of fit through tools like Q-Q plots, the Kolmogorov-Smirnov test, and the Anderson-Darling statistic, often comparing several candidate distributions before selecting the one that best captures both the body and tail of the data. Once calibrated, the severity distribution feeds into aggregate loss models — frequently via [[Definition:Monte Carlo simulation | Monte Carlo simulation]] — that combine it with a frequency distribution to produce the full loss distribution used for [[Definition:Ratemaking | ratemaking]], [[Definition:Reserve | reserve]] estimation, [[Definition:Reinsurance pricing | reinsurance pricing]], and [[Definition:Economic capital | economic capital]] calculation under frameworks such as [[Definition:Solvency II | Solvency II]] and the [[Definition:Risk-based capital (RBC) | RBC]] system.

💡 Getting the severity distribution right is one of the highest-leverage decisions an actuary makes, because even small misspecifications in the tail can translate into enormous pricing or reserving errors — particularly in long-tail lines like [[Definition:Directors and officers insurance (D&O) | D&O]], [[Definition:Medical malpractice insurance | medical malpractice]], and [[Definition:Excess of loss reinsurance | excess-of-loss reinsurance]] where a single outsized claim can dwarf hundreds of smaller ones. Regulatory and rating-agency scrutiny has intensified around tail-risk modeling: [[Definition:Internal model | internal models]] submitted to supervisors under Solvency II, for instance, must demonstrate that their severity assumptions are well-supported by data and expert judgment. As the industry accumulates richer data through [[Definition:Insurtech | insurtech]] platforms and [[Definition:Telematics | telematics]], actuaries are increasingly exploring non-parametric and machine-learning approaches that relax traditional distributional assumptions, though parametric severity models remain the lingua franca of insurance pricing worldwide.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Frequency distribution]]
* [[Definition:Aggregate loss distribution]]
* [[Definition:Actuarial science]]
* [[Definition:Loss development]]
* [[Definition:Monte Carlo simulation]]
* [[Definition:Excess of loss reinsurance]]
{{Div col end}}

Definition:Severity distribution - Revision history

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