Calculate Poisson distribution PMF and CDF for a given number of events and rate. Use it to find probabilities of event counts in a fixed interval.
Calculate Poisson distribution PMF and CDF for k events with rate lambda.
| Name | Required | Description | Default |
|---|---|---|---|
| k | Yes | Number of events (non-negative integer). | |
| lambda | Yes | Expected rate (positive). |
Changes observed during successful MCP inspections.
v0.1.11Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It mentions PMF and CDF computation but does not disclose which is returned, whether both are returned, the output format, or any numeric precision behavior.
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?
A single, tight sentence that front-loads the verb and resource. No filler or redundancy.
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?
For a simple two-parameter math tool with 100% schema coverage and no annotations, the description is minimally adequate. It leaves ambiguity about PMF vs CDF output that an agent would want resolved, but the core operation is identifiable.
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 coverage is 100%, so both parameters (k, lambda) are documented in the schema with constraints. The description names lambda and k implicitly but adds no semantic detail beyond what the schema already provides. Baseline 3 is appropriate.
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?
States a specific verb (Calculate) and resource (Poisson distribution PMF and CDF) with the key inputs. Clear what it does, though it does not differentiate itself from sibling binomial_probability or normal_distribution.
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?
No guidance on when to use this versus binomial_probability, normal_distribution, or the many other probability/statistics tools in the catalog. The agent must infer applicability from domain knowledge.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.