MathLiveStudent's t-distribution probability density function
Gives the probability density of a Student's t random variable x with ν degrees of freedom. It is used in statistics for inference on a mean when the population variance is unknown and the sample is small.
f(x) = \frac{\Gamma\left(\frac{\nu + 1}{2}\right)}{\sqrt{\pi \nu}\,\Gamma\left(\frac{\nu}{2}\right)} \left(1 + \frac{x^2}{\nu}\right)^{-\frac{\nu + 1}{2}}What the symbols mean
| probability density at value x | |
| value of the random variable | |
| degrees of freedom (positive) | |
| gamma function | |
| pi, the ratio of a circle's circumference to its diameter |
About this formula
- FieldStatistics
- TopicProbability distributions
- LevelUniversity
- Also calledStudent's t density, t-distribution pdf, Student's t probability density, t-distribution formula, Student's distribution density function, Student's distribution
- SourceWikidata Q576072
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