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Student t

Normal uncertainty with an estimated scale; approaches normal as ν grows.
Type continuousSupport ℝFamily Heavy tail
Probability densityT = Z / √(V/ν)
continuous

Student t in motion

-6.0-3.00.03.06.0
Supportℝ
Mean0
Variance1.667
Connections

Where the student t
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

Cauchyν = 1

Student t with one degree of freedom is standard Cauchy.

Special caseNormalν→∞

As scale estimation uncertainty vanishes, t approaches normal.

Limiting result

Zoom out

See every connection at once.

The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

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