SooTool

probability.exponential_ppf

Read-onlyIdempotent

Computes the exponential distribution quantile x = -ln(1-q)/λ from a probability q and positive rate λ, returning a 10-significant-digit decimal string. Use rate, not mean.

Instructions

지수분포의 분위수 x = -ln(1-q)/λ 를 구한다. q 는 0 초과 1 미만, rate(λ)는 양수 십진 문자열이며 scipy float64 계산 후 유효숫자 10자리로 반올림한 문자열을 반환한다. rate 에 평균(1/λ)을 넣으면 틀린다.

Input Schema

Name	Required	Description	Default
`q`	Yes
`rate`	Yes

Output Schema

Name	Required	Description
`_meta`	No	서버가 붙이는 영수증(integrity), 엔진, 힌트
`trace`	Yes	계산 근거(tool, formula, inputs, steps, output)
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv0.3.0Oct 29, 2026

TDQS

A4.4/5.0

Behavior4/5

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

Annotations already cover readOnly/idempotent/closed-world safety, so the description's added value is real: it discloses the scipy float64 computation and that results are returned as a string rounded to 10 significant digits. That output-shape detail is behavior beyond what the annotations declare, though it stops short of error behavior for invalid inputs.

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

Conciseness5/5

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

Three sentences, front-loaded with the formula, then input constraints, then the mean-vs-rate pitfall. Every sentence contributes a distinct fact with no redundancy.

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

Completeness5/5

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

For a two-parameter scalar math tool this is complete: formula, parameter domains/formats, the mean-rate trap, and return format are all stated, and the output schema covers the return type. An agent can call it correctly from the description alone.

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

Parameters5/5

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

Schema coverage is 0% (parameters are bare 'Q' and 'Rate'), so the description carries the full burden and does: q must be strictly between 0 and 1, rate(λ) must be a positive decimal string, and it explicitly warns not to substitute the mean 1/λ. Both parameters get format and semantic meaning the schema lacks.

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

Purpose5/5

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

States a specific operation (exponential-distribution quantile) and immediately gives the closed form x = -ln(1-q)/λ, which unambiguously separates it from sibling CDF/PDF tools like probability.exponential_cdf and probability.exponential_pdf. No schema-open needed to know what it computes.

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

Usage Guidelines3/5

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

Usage is implied by the formula and the domain constraints (0<q<1, λ>0), and the warning that passing the mean 1/λ as rate is wrong is a useful guardrail against a common error. However, it never names when to pick this over siblings or states preconditions beyond parameter validity.

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

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