hasMomentGeneratingFunction
P27171
predicate
Indicates that a random variable or probability distribution possesses a well-defined moment generating function characterizing all of its moments.
All labels observed (2)
| Label | Occurrences |
|---|---|
| momentGeneratingFunction | 4 |
| hasMomentGeneratingFunction canonical | 3 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasMomentGeneratingFunction
Generated description
Indicates that a random variable or probability distribution possesses a well-defined moment generating function characterizing all of its moments.
Sample triples (7)
| Subject | Object |
|---|---|
| Gaussian distribution | M(t) = exp(μt + ½σ²t²) ⓘ |
| Laplace law of error | M(t) = exp(μ t) / (1 - b^2 t^2) for |t| < 1/b via predicate surface "momentGeneratingFunction" ⓘ |
| Cauchy distribution | does not exist ⓘ |
| Bernoulli distribution | M(t)=1-p+pe^t via predicate surface "momentGeneratingFunction" ⓘ |
| chi-square distribution | M(t) = (1 - 2t)^{-k/2} for t < 1/2 via predicate surface "momentGeneratingFunction" ⓘ |
| Laplace distribution | M(t) = 1 / (1 - b^2 t^2) for |t| < 1/b via predicate surface "momentGeneratingFunction" ⓘ |
| double exponential distribution | M(t) = exp(μ t) / (1 - b^2 t^2), |t| < 1/b ⓘ |