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agmonetti

mathmethods-mcp

by agmonetti

mc_estadistico_1d

Runs replicated Monte Carlo integration to estimate definite integrals and compute confidence intervals from the distribution of estimates.

Instructions

Replicated Monte Carlo experiment (M repetitions of N samples) with statistical analysis.

Args: func_str: Math expression in x. a, b: Integration limits (b > a). N: Samples per replication. M: Number of replications. nivel_confianza: Confidence level in (0, 1). seed: Optional RNG seed. precision: Rounding digits.

Returns: Dict with the distribution of estimates and confidence intervals.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
MNo
NNo
aYes
bYes
seedNo
func_strYes
precisionNo
nivel_confianzaNo
Install Server

TDQS

A3.8/5.0
Behavior3/5

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It does mention the repetition structure, seed optionality, confidence-level range, rounding, and a dict return, but it omits details about the exact sampling algorithm, error handling, output keys, or side effects. This is reasonably transparent but not fully complete.

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?

The description is a tight docstring with a one-sentence summary followed by an organized Args list and a Returns line. Every line adds necessary information, with no redundancy or filler.

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

Completeness3/5

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

Without an output schema or annotations, the description needs to fully explain the return value, but it only says 'Dict with the distribution of estimates and confidence intervals' without specifying keys, units, or how the distribution is summarized. The parameter list is complete, but the output shape remains under-specified, which limits how well an agent can interpret the result.

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 description coverage is 0%, so the description is essential and fully compensates. Every parameter gets a concise semantic explanation: func_str as a math expression, a and b as integration limits with b > a, N/M as sample/replication counts, nivel_confianza as a confidence level in (0,1), seed as optional RNG seed, and precision as rounding digits. This goes far beyond the bare schema and enables correct invocation.

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?

The description clearly identifies this as a replicated Monte Carlo experiment with statistical analysis for a 1D integral, which conveys the core purpose. However, it does not explicitly differentiate itself from sibling MC tools like mc_valor_promedio_1d or mc_convergencia_1d, leaving some ambiguity about the specific niche beyond the word 'estadistico'.

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 description implies usage when a user wants a distribution of estimates over M repetitions rather than a single estimate or convergence assessment, but it provides no explicit when-to-use or when-not-to-use guidance. It also does not mention alternative sibling tools or criteria for choosing this tool over them.

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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