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📋 '''Lognormal distribution''' is a continuous probability distribution widely used in [[Definition:Actuarial science | actuarial science]] and insurance [[Definition:Risk modeling | risk modeling]] to represent variables — particularly individual [[Definition:Claims | claim]] sizes — that are always positive, right-skewed, and exhibit a long upper tail. Because the natural logarithm of a lognormally distributed variable follows a [[Definition:Normal distribution | normal distribution]], it provides a mathematically tractable yet realistic way to capture the empirical pattern seen in many insurance portfolios: a concentration of moderate losses with an extended tail of large, infrequent ones.

⚙️ [[Definition:Actuary | Actuaries]] fit lognormal models to historical [[Definition:Loss data | loss data]] by estimating two parameters — the mean and standard deviation of the log-transformed values — typically through [[Definition:Maximum likelihood estimation | maximum likelihood estimation]] or method-of-moments techniques. Once calibrated, the distribution feeds into [[Definition:Loss distribution | aggregate loss models]], [[Definition:Reinsurance pricing | reinsurance pricing]] layers, and [[Definition:Stochastic model | stochastic simulations]] that test tail scenarios. In [[Definition:Property insurance | property]] and [[Definition:Casualty insurance | casualty]] lines, it often serves as the severity component within a frequency-severity framework, paired with a [[Definition:Poisson distribution | Poisson]] or [[Definition:Negative binomial distribution | negative binomial]] frequency assumption. [[Definition:Catastrophe model | Catastrophe modelers]] and [[Definition:Enterprise risk management (ERM) | enterprise risk management]] teams also rely on lognormal assumptions when simulating investment returns or [[Definition:Inflation | inflation]] factors embedded in [[Definition:Loss reserve | reserve]] projections.

💡 Choosing the right distributional form is far from an academic exercise — it directly affects how much [[Definition:Capital | capital]] an insurer holds, what [[Definition:Premium | premium]] it charges, and how it structures [[Definition:Reinsurance | reinsurance]] treaties. The lognormal distribution's ability to capture heavy tails makes it a natural starting point, but practitioners must remain alert to its limitations: extremely heavy-tailed lines such as [[Definition:Excess liability insurance | excess liability]] or [[Definition:Cyber insurance | cyber]] may be better served by [[Definition:Pareto distribution | Pareto]] or other heavy-tailed alternatives. Rigorous goodness-of-fit testing and scenario analysis ensure that model outputs translate into sound [[Definition:Underwriting | underwriting]] and [[Definition:Reserving | reserving]] decisions rather than false precision.

'''Related concepts'''
{{Div col|colwidth=20em}}
* [[Definition:Loss distribution]]
* [[Definition:Pareto distribution]]
* [[Definition:Actuarial science]]
* [[Definition:Stochastic model]]
* [[Definition:Severity]]
* [[Definition:Tail risk]]
{{Div col end}}

Definition:Lognormal distribution - Revision history

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