SooTool

probability.beta_pdf

Read-onlyIdempotent

Computes the beta distribution probability density f(x; α, β) for x in [0, 1] and positive decimal α, β, returning a rounded numeric string; the value is a density, not a probability.

Instructions

베타분포의 확률밀도 f(x; α, β)를 구한다. x 는 [0, 1] 구간, alpha 와 beta 는 양수 십진 문자열이며 scipy float64 계산 후 유효숫자 10자리로 반올림한 문자열을 반환한다. 밀도값은 1 을 넘을 수 있고 확률이 아니다.

Input Schema

Name	Required	Description	Default
`x`	Yes
`beta`	Yes
`alpha`	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

A3.9/5.0

Behavior4/5

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

Annotations already cover the safety profile (readOnly, idempotent, closed-world). The description adds real context beyond them: computation is done in scipy float64 and the result is rounded to 10 significant digits, returned as a string. The warning that density values can exceed 1 and are not probabilities is a genuinely useful behavioral clarification.

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 tight sentences, front-loaded with the definition, then input domain, then return format, then the mis-interpretation warning. No repetition of the tool name or filler.

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

Completeness4/5

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

An output schema exists, so return values need not be explained, yet the description still describes the string/rounding contract. Remaining gaps are edge-case behavior: no statement of what is returned or raised when x falls outside [0,1] or alpha/beta are non-positive.

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

Parameters4/5

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

Schema description coverage is 0%, so the description carries the full burden, and it does: x is constrained to [0,1], and alpha/beta are described as positive decimal strings, telling the agent to pass strings rather than numbers. It does not explicitly state that x is also a string, a small residual gap.

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

Purpose4/5

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

States a precise verb+resource: computes the beta distribution probability density f(x; α, β). The word '밀도'(density) inherently separates it from the sibling beta_cdf and beta_ppf, though those alternatives are never named. A clear purpose, but without explicit sibling differentiation.

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?

The domain constraints (x in [0,1], alpha/beta positive) imply when the tool is applicable, but there is no explicit statement of when to use this versus beta_cdf/beta_ppf, nor any note on what happens for out-of-range input. Usage must be inferred.

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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