{
    "api": "YAML JSON TOON Database",
    "version": "1.0.0",
    "format": "json",
    "dataset": {
        "id": 1646,
        "slug": "probability-distribution-reference",
        "title": "Probability Distribution Selection Reference",
        "description": "Common probability distributions with support, mean, and practical modeling boundaries.",
        "summary": "Common probability distributions with support, mean, and practical modeling boundaries. Each row includes a practical application and a failure to check before using it.",
        "use_when": [
            "Choose a distribution by support and mechanism.",
            "Check parameter conventions before comparing implementations."
        ],
        "caveats": [
            "All parameters must satisfy the distribution\u2019s domain constraints.",
            "A good fit does not establish the mechanism that generated the data."
        ],
        "related": [
            "experimental-design-pitfalls",
            "statistics-basics"
        ],
        "reviewed_at": "2026-10-12",
        "sources": [
            {
                "title": "NIST probability distributions handbook",
                "url": "https:\/\/www.itl.nist.gov\/div898\/handbook\/eda\/section3\/eda36.htm"
            }
        ],
        "reading": [
            "choose-a-probability-distribution-with-explicit-assumptions"
        ],
        "provenance": "Original editorial reference notes by YJTOON, informed by the linked primary documentation. External specifications retain their own licenses.",
        "entry_count": 10,
        "fields": [
            {
                "section": "data",
                "field": "distribution",
                "type": "string",
                "example": "Bernoulli(p)"
            },
            {
                "section": "data",
                "field": "support",
                "type": "string",
                "example": "0 or 1"
            },
            {
                "section": "data",
                "field": "mean",
                "type": "string",
                "example": "p"
            },
            {
                "section": "data",
                "field": "use_and_boundary",
                "type": "string",
                "example": "One binary trial; define what counts as success."
            }
        ],
        "category": "Mathematics",
        "category_slug": "mathematics",
        "tags": "mathematics,probability distribution reference,reference,engineering",
        "view_count": 11,
        "created_at": 1791798640,
        "updated_at": 1791798640
    },
    "data": [
        {
            "distribution": "Bernoulli(p)",
            "support": "0 or 1",
            "mean": "p",
            "use_and_boundary": "One binary trial; define what counts as success."
        },
        {
            "distribution": "Binomial(n,p)",
            "support": "Integers 0 through n",
            "mean": "n*p",
            "use_and_boundary": "Count successes in n independent equal-probability trials."
        },
        {
            "distribution": "Geometric(p)",
            "support": "Integers 1 and above",
            "mean": "1\/p",
            "use_and_boundary": "Count trials until first success; another convention counts failures from zero."
        },
        {
            "distribution": "Poisson(lambda)",
            "support": "Nonnegative integers",
            "mean": "lambda",
            "use_and_boundary": "Count events under a constant-rate independent-increment model."
        },
        {
            "distribution": "Exponential(lambda)",
            "support": "Nonnegative real values",
            "mean": "1\/lambda",
            "use_and_boundary": "Model memoryless waiting time; not every duration is memoryless."
        },
        {
            "distribution": "Uniform(a,b)",
            "support": "Real values from a to b",
            "mean": "(a+b)\/2",
            "use_and_boundary": "Equal density on a bounded interval; endpoints have zero point probability."
        },
        {
            "distribution": "Normal(mu,sigma)",
            "support": "All real values",
            "mean": "mu",
            "use_and_boundary": "Model symmetric fluctuations; negative values may be inappropriate for some quantities."
        },
        {
            "distribution": "Lognormal(mu,sigma)",
            "support": "Positive real values",
            "mean": "exp(mu+sigma^2\/2)",
            "use_and_boundary": "Model positive multiplicative variability; parameters describe the underlying normal."
        },
        {
            "distribution": "Beta(alpha,beta)",
            "support": "Real values from 0 to 1",
            "mean": "alpha\/(alpha+beta)",
            "use_and_boundary": "Model a bounded proportion with positive shape parameters."
        },
        {
            "distribution": "Gamma(shape,scale)",
            "support": "Positive real values",
            "mean": "shape*scale",
            "use_and_boundary": "Model positive skewed quantities; rate and scale parameterizations differ."
        }
    ]
}