Probability Distribution Selection Reference
Common probability distributions with support, mean, and practical modeling boundaries.
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 it when
- Choose a distribution by support and mechanism.
- Check parameter conventions before comparing implementations.
Watch out for
- All parameters must satisfy the distribution’s domain constraints.
- A good fit does not establish the mechanism that generated the data.
The data
10 rows
| 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. |
Fields
The shape of this dataset, read from the data itself: every column, its type and a real value. Agents can use this to plan a query without fetching the whole document.
| 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. |
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Sources and editorial notes
Original editorial reference notes by YJTOON, informed by the linked primary documentation. External specifications retain their own licenses.
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