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📊 '''Pareto distribution''' is a heavy-tailed statistical distribution widely used in insurance to model the frequency and severity of large losses, particularly in lines such as [[Definition:Property insurance | property]], [[Definition:Liability insurance | liability]], and [[Definition:Catastrophe risk | catastrophe risk]]. Named after economist Vilfredo Pareto, the distribution captures the empirical reality that a small number of claims often account for a disproportionately large share of total losses — a phenomenon sometimes expressed as the "80/20 rule." [[Definition:Actuary | Actuaries]] rely on it when the tail of the [[Definition:Loss distribution | loss distribution]] is more important than the body, which is common in [[Definition:Excess of loss reinsurance | excess-of-loss reinsurance]] pricing and [[Definition:Large loss | large-loss]] analysis.

⚙️ In practice, fitting a Pareto distribution to historical [[Definition:Claims data | claims data]] involves estimating a shape parameter (often denoted α) and a scale or threshold parameter. A lower α indicates a heavier tail, meaning extreme losses are relatively more likely — a critical insight when setting [[Definition:Retention | retentions]], pricing [[Definition:Reinsurance | reinsurance]] layers, or calibrating [[Definition:Internal model | internal models]] for [[Definition:Solvency II | Solvency II]] capital requirements. Actuaries often use the Pareto distribution alongside other heavy-tailed models such as the [[Definition:Lognormal distribution | lognormal]] or [[Definition:Generalized Pareto distribution | generalized Pareto distribution]], selecting whichever best fits the observed data above a chosen threshold. It is especially useful in [[Definition:Treaty reinsurance | treaty reinsurance]] negotiations, where both cedants and reinsurers need to agree on expected losses in high layers where data is sparse.

💡 Understanding tail behavior is not merely an academic exercise — it directly affects an insurer's financial resilience. Underestimating the heaviness of the loss tail can lead to inadequate [[Definition:Technical provisions | technical provisions]], mispriced [[Definition:Premium | premiums]], and unexpected [[Definition:Capital adequacy | capital]] strain after a series of large events. Regulators and [[Definition:Rating agency | rating agencies]] scrutinize the distributional assumptions embedded in an insurer's [[Definition:Risk model | risk models]], and the Pareto distribution remains one of the most transparent and well-understood tools for communicating tail risk. Its simplicity also makes it a valuable benchmark: even when more complex models are used, comparing results against a fitted Pareto provides a useful sanity check.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Loss distribution]]
* [[Definition:Excess of loss reinsurance]]
* [[Definition:Actuarial modeling]]
* [[Definition:Tail risk]]
* [[Definition:Generalized Pareto distribution]]
* [[Definition:Catastrophe model]]
{{Div col end}}

Definition:Pareto distribution - Revision history

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