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<p>Bot: Creating new article from JSON</p> <p><b>New page</b></p><div>📊 &#039;&#039;&#039;Gamma distribution&#039;&#039;&#039; is a continuous probability distribution widely used by [[Definition:Actuary | actuaries]] and [[Definition:Catastrophe modeler | catastrophe modelers]] to represent the aggregate severity or frequency of [[Definition:Claims | claims]] in an [[Definition:Insurance | insurance]] portfolio. Because its shape can range from highly skewed to nearly symmetric depending on its parameters, the gamma distribution adapts well to the kinds of loss data insurers encounter — where most claims are small but a heavy tail of large losses exerts outsized influence on overall [[Definition:Loss ratio (L/R) | loss ratios]].<br /> <br /> 🔢 In practice, an actuary fits a gamma distribution to historical [[Definition:Loss | loss]] data by estimating two parameters: a shape parameter and a scale (or rate) parameter. The shape parameter controls how peaked or spread the distribution is, while the scale parameter stretches or compresses it along the monetary axis. Once calibrated, the model can simulate thousands of potential outcomes for [[Definition:Reserve | reserve]] adequacy testing, [[Definition:Reinsurance pricing | reinsurance pricing]], or [[Definition:Capital modeling | capital modeling]] exercises. It often appears as a building block inside more complex frameworks — for example, when combined with a [[Definition:Poisson distribution | Poisson distribution]] for claim counts, it produces a compound Poisson–gamma model that many [[Definition:Property and casualty insurance (P&amp;C) | property and casualty]] teams rely on for aggregate loss projections.<br /> <br /> 📈 Getting the distributional assumption right carries real financial consequences. If an insurer underestimates tail thickness by choosing a distribution that is too thin — or miscalibrates the gamma&#039;s shape parameter — it may set [[Definition:Premium | premiums]] too low or hold insufficient [[Definition:Technical provisions | technical provisions]], exposing itself to [[Definition:Solvency | solvency]] stress. Regulators and [[Definition:Rating agency | rating agencies]] scrutinize these modeling choices during reviews, and [[Definition:Reinsurer | reinsurers]] challenge them when negotiating treaty terms. The gamma distribution endures as a standard tool precisely because it strikes a practical balance between mathematical tractability and fidelity to observed insurance loss behavior.<br /> <br /> &#039;&#039;&#039;Related concepts:&#039;&#039;&#039;<br /> {{Div col|colwidth=20em}}<br /> * [[Definition:Actuarial science]]<br /> * [[Definition:Loss distribution]]<br /> * [[Definition:Poisson distribution]]<br /> * [[Definition:Tail risk]]<br /> * [[Definition:Stochastic modeling]]<br /> * [[Definition:Aggregate loss]]<br /> {{Div col end}}</div>

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