Runtime (Severity)

This page explains common severity models used in CRML scenarios.

CRML severity is expressed as:

• scenario.severity.model: a model identifier (engine-defined support)
• scenario.severity.parameters: model parameters (portable intent; engine may impose constraints)

See: Scenario schema

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Lognormal

A lognormal model is common for heavy-tailed loss severities.

If $X$ is the loss per event, then:

$$\ln X \sim \mathcal{N}(\mu, \sigma^2)$$

CRML commonly uses a median-first parameterization for readability:

• median: the median loss ($\text{median}(X)$)
• sigma: log-space standard deviation

Relationship between median and $\mu$:

$$\text{median}(X) = e^{\mu} \quad \Rightarrow \quad \mu = \ln(\text{median}(X))$$

Empirical calibration (single_losses)

Some engines may support calibrating $(\mu, \sigma)$ from empirical single-event losses.

Reference engine status:

• Calibration helper exists: crml_engine.runtime.calibrate_lognormal_from_single_losses.
• You can also provide single_losses directly in lognormal parameters (engine-defined behavior).

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Gamma

A gamma distribution is another positive-valued severity model.

Common parameterization uses shape ($k$) and scale ($\theta$):

$$X \sim \text{Gamma}(k, \theta)$$

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Mixtures

A mixture model represents severity as a weighted combination of component distributions.

Conceptually, you choose a component $C$ with probability $w_c$ and then sample $X \mid C$.

Important: mixture support is engine-defined.

Reference engine limitation:

• The current reference engine’s mixture severity uses only the first component and ignores weights.

See: Engine capabilities: Supported models