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📊 '''Frequency distribution''' is a statistical tool used extensively in [[Definition:Actuarial science | actuarial science]] and insurance analytics to describe how often losses of various sizes or types occur within a defined portfolio or exposure period. Rather than examining individual claims in isolation, actuaries organize historical [[Definition:Loss | loss]] data into a structured representation — often a table, histogram, or fitted probability model — that reveals the pattern of claim counts across severity bands, time intervals, or peril categories. Common probability distributions employed to model claim frequency in insurance include the Poisson distribution (for relatively rare, independent events), the negative binomial distribution (when claim counts exhibit overdispersion), and the binomial distribution (for fixed exposure counts), each chosen based on the characteristics of the underlying data.

⚙️ In practice, actuaries fit frequency distributions to observed claims data as one half of the frequency-severity modeling framework that underpins most [[Definition:Ratemaking | ratemaking]], [[Definition:Reserving | reserving]], and [[Definition:Catastrophe modeling | catastrophe modeling]] exercises. The frequency component captures how many claims are expected, while a separate [[Definition:Severity distribution | severity distribution]] captures how large each claim is likely to be; combining the two through techniques such as collective risk modeling or Monte Carlo simulation produces an aggregate loss distribution that informs [[Definition:Premium | pricing]], [[Definition:Reinsurance | reinsurance]] structuring, and [[Definition:Capital allocation | capital allocation]]. Under regulatory frameworks like [[Definition:Solvency II | Solvency II]] and [[Definition:Risk-based capital (RBC) | risk-based capital]] regimes, insurers must demonstrate that their internal models use statistically sound frequency assumptions, calibrated to credible data and stress-tested against adverse scenarios. The choice of distribution matters enormously — misspecifying frequency can lead to systematic underpricing or overpricing of an entire book of business.

🔑 A well-calibrated frequency distribution gives insurers a quantitative foundation for nearly every strategic and operational decision they make. It informs how much [[Definition:Premium | premium]] to charge, how much [[Definition:Reserve | reserve]] to hold, when to purchase [[Definition:Excess of loss reinsurance | excess of loss reinsurance]], and how to allocate capital across lines of business. With the expansion of [[Definition:Telematics | telematics]], IoT sensors, and other real-time data sources, insurers and [[Definition:Insurtech | insurtechs]] are increasingly able to refine frequency estimates at granular levels — per policyholder, per geography, or even per driving trip — enabling more precise segmentation and dynamic pricing. The ongoing evolution of data availability and computational power continues to sharpen the insurance industry's ability to understand and predict claim frequency, which remains one of the most fundamental building blocks of the actuarial craft.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Severity distribution]]
* [[Definition:Actuarial science]]
* [[Definition:Ratemaking]]
* [[Definition:Aggregate loss distribution]]
* [[Definition:Catastrophe modeling]]
* [[Definition:Loss ratio (L/R)]]
{{Div col end}}

Definition:Frequency distribution - Revision history

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