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📊 '''Maximum likelihood estimation''' is a statistical method widely used by [[Definition:Actuary | actuaries]] and insurance data scientists to estimate the parameters of probability distributions that model [[Definition:Loss | loss]] frequency, [[Definition:Loss severity | severity]], and other key risk variables. At its core, the technique identifies the set of parameter values that makes the observed data most probable under a given distributional assumption — in insurance terms, it finds the best-fitting model for historical [[Definition:Claim | claims]] data. The method underpins much of modern [[Definition:Actuarial science | actuarial science]], from [[Definition:Pricing | pricing]] individual [[Definition:Policy | policies]] to calibrating enterprise-wide [[Definition:Catastrophe model | catastrophe models]].

⚙️ In practice, an actuary might assume that claims follow a [[Definition:Probability distribution | probability distribution]] — say, a lognormal or Pareto distribution — and then apply maximum likelihood estimation to historical loss data to determine the distribution's parameters (such as mean and variance). The algorithm constructs a likelihood function representing the probability of observing the actual data given various parameter values, then optimizes to find the parameter set that maximizes this function. This fitted distribution can then be used to project future [[Definition:Loss ratio (L/R) | loss ratios]], set [[Definition:Reserve | reserves]], calculate [[Definition:Reinsurance | reinsurance]] layer pricing, or stress-test portfolios under adverse scenarios. Software tools embedded in [[Definition:Actuarial software | actuarial platforms]] and [[Definition:Insurtech | insurtech]] analytics suites automate this process, allowing rapid recalibration as new data arrives.

💡 The reliability of insurance decisions — from [[Definition:Premium | premium]] adequacy to [[Definition:Solvency | solvency]] capital requirements — depends heavily on how well the underlying statistical models represent reality. Maximum likelihood estimation earns its central role because it produces estimates with desirable mathematical properties: they are consistent, asymptotically efficient, and lend themselves to straightforward confidence interval construction. However, the technique is only as good as the distributional assumption it starts with; fitting a model to thin or volatile data — common in [[Definition:Specialty insurance | specialty lines]] or emerging risks like [[Definition:Cyber insurance | cyber]] — requires careful judgment. Regulatory frameworks such as [[Definition:Solvency II | Solvency II]] expect insurers to demonstrate that their internal models are statistically sound, making rigorous parameter estimation not just a technical exercise but a compliance imperative.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Actuarial science]]
* [[Definition:Probability distribution]]
* [[Definition:Loss severity]]
* [[Definition:Catastrophe model]]
* [[Definition:Credibility theory]]
* [[Definition:Generalized linear model (GLM)]]
{{Div col end}}

Definition:Maximum likelihood estimation - Revision history

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