api: YAML JSON TOON Database
version: 1.0.0
format: toon
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[2]: Choose a distribution by support and mechanism.,Check parameter conventions before comparing implementations.
  caveats[2]: All parameters must satisfy the distribution’s domain constraints.,A good fit does not establish the mechanism that generated the data.
  related[2]: experimental-design-pitfalls,statistics-basics
  reviewed_at: 2026-10-12
  sources[1]{title,url}:
    NIST probability distributions handbook,"https://www.itl.nist.gov/div898/handbook/eda/section3/eda36.htm"
  reading[1]: 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[4]{section,field,type,example}:
    data,distribution,string,Bernoulli(p)
    data,support,string,0 or 1
    data,mean,string,p
    data,use_and_boundary,string,One binary trial; define what counts as success.
  category: Mathematics
  category_slug: mathematics
  tags: "mathematics,probability distribution reference,reference,engineering"
  view_count: 2
  created_at: 1791798640
  updated_at: 1791798640
data[10]{distribution,support,mean,use_and_boundary}:
  Bernoulli(p),0 or 1,p,One binary trial; define what counts as success.
  "Binomial(n,p)",Integers 0 through n,n*p,Count successes in n independent equal-probability trials.
  Geometric(p),Integers 1 and above,1/p,Count trials until first success; another convention counts failures from zero.
  Poisson(lambda),Nonnegative integers,lambda,Count events under a constant-rate independent-increment model.
  Exponential(lambda),Nonnegative real values,1/lambda,Model memoryless waiting time; not every duration is memoryless.
  "Uniform(a,b)",Real values from a to b,(a+b)/2,Equal density on a bounded interval; endpoints have zero point probability.
  "Normal(mu,sigma)",All real values,mu,Model symmetric fluctuations; negative values may be inappropriate for some quantities.
  "Lognormal(mu,sigma)",Positive real values,exp(mu+sigma^2/2),Model positive multiplicative variability; parameters describe the underlying normal.
  "Beta(alpha,beta)",Real values from 0 to 1,alpha/(alpha+beta),Model a bounded proportion with positive shape parameters.
  "Gamma(shape,scale)",Positive real values,shape*scale,Model positive skewed quantities; rate and scale parameterizations differ.