Description
Classify the Beta density at zero from its positive first shape parameter, holding the second shape positive.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
Classify the Beta density at zero from its positive first shape parameter, holding the second shape positive.
When to use this tool
Use Beta Density Endpoint Power Test when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
How to use the tool and how it works
- Enter shape. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read limit, integrable. Inspect integrable before interpreting the associated values.
For positive first Beta shape return limit=infinite below one, finite-nonzero at one, or zero above one; integrable is always true.1
For the standard Beta distribution the density contains x^(alpha-1). With the other shape positive, this power controls the zero-endpoint classification used here.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| shape | Positive first Beta shape alpha; the second shape is assumed positive. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| limit | Density limit at zero: infinite, finite-nonzero, or zero. | Required. Text; maximum UTF-16 length 8192. |
| integrable | Always true for the accepted positive shape. | Required. Boolean. |
{
"input": {
"shape": 0.5
},
"output": {
"limit": "infinite",
"integrable": true
}
}Limitations and assumptions
- This describes the density limit at zero while the second Beta shape is assumed positive. No numerical density, normalization constant, or behavior at the opposite endpoint is calculated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
-
Calculation and input contract: probability/beta-density-endpoint-power-test — tool.io
-
NIST/SEMATECH e-Handbook: Beta Distribution — National Institute of Standards and Technology
Similar or alternative tools
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For probability strictly between zero and one return information=1/(probability*(1-probability)).
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Return lowerMode=clamp(ceil(a)-1,0,trials), upperMode=min(trials,floor(a)), and tied when a is an integer from one through trials.