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name: distributions-logprob description: "Choose, parameterize, shape, extend, and validate PyMC distributions and log-probability graphs." disable-model-invocation: true metadata: disco-role: operating license: NOASSERTION

PyMC distributions and log-probability graphs

Use this sub-skill when the task is to choose a PyMC probability distribution, parameterize it, reason about shape/size/dims and support dimensions, build unregistered component distributions with .dist(), define a CustomDist/DensityDist, or inspect pm.logp / pm.logcdf graphs.

Operating checklist

1. Decide whether the variable should be registered (pm.Normal("x", ...)) or an unregistered component (pm.Normal.dist(...)). Components for mixtures, truncation, censoring, and symbolic custom graphs should almost always use .dist().
2. Choose the family by support and dependency structure: continuous, discrete, multivariate, time-series, mixture/zero-inflated/hurdle, censored/truncated, simulator, or custom.
3. Set shape/size/dims deliberately. dims belongs to registered model variables; .dist(dims=...) is not supported.
4. Validate support, parameter domains, broadcasting, transforms, and initial values before spending time on inference.
5. For custom distributions, provide consistent logp, optional random, optional logcdf, optional support_point, and signature/ndims_params when support or parameter dimensions are not scalar.

Bundled resources

• Read references/distribution-workflows.md for choosing distribution families, .dist(), shapes/dims/support dimensions, and custom distributions.
• Read references/api-reference.md for verified signatures and parameter notes.
• Read references/troubleshooting.md for mixture, custom logp, transform, support point, or broadcasting errors.
• Run scripts/distribution_logp_smoke.py for a tiny safe smoke of CustomDist, mixture .dist() components, pm.logp, and shape output.

Route elsewhere

• General model context/data mutation: ../modeling-data/SKILL.md.
• Sampling and posterior predictive execution: ../inference-predictive/SKILL.md.
• Gaussian-process modeling family details: ../advanced-workflows/SKILL.md.