Random Weighted Bucket Member Draw

Description

Choose an explicit positive-weight bucket, then a uniform member position within it; not uniform over all flattened members. Zero-weight empty buckets permitted.

A random construction is defined by its sampling support: positions, permutations, complete tilings, proposal sequences or another explicit set. Uniform choices at one stage do not necessarily make final visible outcomes uniform. A replay seed gives a deterministic sequence; equal values can hide different sampled positions. These tools are for reproducible synthetic examples rather than cryptographic entropy.

Choose an explicit positive-weight bucket, then a uniform member position within it; not uniform over all flattened members. Zero-weight empty buckets permitted.

When to use this tool

Use this tool to choose an explicit positive-weight bucket, then a uniform member position within it; not uniform over all flattened members. Zero-weight empty buckets permitted.

How to use the tool and how it works

Enter bucketsJson, weights, seed using the definitions below. Serialize JSON text fields in the decoded shape shown below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.seed, result.bucket, result.position, result.value, using the stated boundary, ordering, sign and absence conventions.

Choose a bucket in proportion to its nonnegative supplied weight, then draw a uniform position within that bucket. Return bucket, position and value.^[1]

Input field	Meaning and units	Accepted input
bucketsJson	JSON array of literal string-member arrays; nonempty/zero-weight rules are stated above.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.
weights	Nonnegative bucket weights aligned with buckets; total must be positive and finite.	Dense list of at most 128 finite numbers, under the stated integer/range rules.
seed	Nonblank replay seed, at most 256 UTF-16 code units; an injected source overrides seeded draws.	Text, at most 8,192 UTF-16 code units; narrower grammar/range rules also apply.

These decoded structures show the examples inside JSON text fields. Supply their serialized JSON strings as input.

json

{
  "bucketsJson": [
    [
      "a",
      "b"
    ],
    [
      "c"
    ]
  ]
}

Output field	Interpretation
result	Object containing the fields below.
result.seed	Original supplied seed string; injected-source replay additionally requires that source’s state.
result.bucket	Zero-based selected bucket index.
result.position	Zero-based selected member position within its original bucket.
result.value	Selected literal member or exact integer text, under the stated generator.

json

{
  "input": {
    "bucketsJson": "[[\"a\",\"b\"],[\"c\"]]",
    "weights": [
      0,
      1
    ],
    "seed": "batch56"
  },
  "output": {
    "result": {
      "seed": "batch56",
      "bucket": 1,
      "position": 0,
      "value": "c"
    }
  }
}

Limitations and assumptions

Weights must have a positive finite total. An empty bucket is allowed only with weight zero; flattened members generally have unequal probabilities.
A nonblank seed of at most 256 UTF-16 code units is required. With ordinary use the seed initializes one deterministic advancing source; an application-injected random source takes precedence and the seed alone then cannot replay the result. Uniformity statements assume independent uniform source draws in [0,1). Source calls are bounded and degenerate injected sources can fail a rejection budget. This is not cryptographically secure.
Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
Ordinary numeric outputs must be finite and within safe-integer magnitude. Exact large lengths/counts use decimal strings. Original record indexes and code-unit positions are zero-based; span ends are exclusive unless stated otherwise.

Alternative or Complementary methods

Choose a generator whose support matches the intended experiment and retain source-position provenance. Use a separate statistically justified process model or cryptographic source where those properties matter.

References

Tool behavior and example: Random Weighted Bucket Member Draw — tool.io

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