distribution

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden of behavioral disclosure. It explains that type selects a screen and that all variables needed by that type must be passed, but it does not describe output behavior, error conditions, or side effects. This is acceptable for a calculator-like tool but lacks richer context.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is well-structured and front-loaded: it starts with the key usage condition, then an alternative, then parameter handling rules, a type list, and an example. Every sentence adds value without unnecessary prose or repetition.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

While the description is helpful, it does not enumerate every valid type string (using wildcards like poisson_* and geometric_*), and some type-specific parameter mappings are omitted. Given the tool's complexity and the lack of enums in the schema, this incompleteness could make it hard for an agent to know exactly which type values and parameters are valid.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It does so by listing type signatures (e.g., normal_pd (x,sigma,mu)) and providing a concrete example, which meaningfully maps parameters to usage. However, not every parameter or type signature is fully spelled out (e.g., inverse_binomial, poisson_*), leaving some gaps.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies the tool as handling probability densities, CDFs, inverses, and standardized t values. It explicitly distinguishes this tool from stats_1var for normal distribution from a data list, making the intended use unambiguous.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description opens with 'When' to define the exact use context, and explicitly says to use stats_1var(norm_x=…) instead for normal distribution from a data list. This provides clear guidance on when to use this tool versus alternatives.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.