Index: The Book of Statistical ProofsProbability Distributions ▷ Univariate continuous distributions ▷ t-distribution ▷ Non-standardized t-distribution

Definition: Let $X$ be a random variable following a Student’s t-distribution with $\nu$ degrees of freedom. Then, the random variable

\[\label{eq:Y} Y = \sigma X + \mu\]

is said to follow a non-standardized t-distribution with non-centrality $\mu$, scale $\sigma^2$ and degrees of freedom $\nu$:

\[\label{eq:nct} Y \sim \mathrm{nst}(\mu, \sigma^2, \nu) \; .\]

Metadata: ID: D152 | shortcut: nst | author: JoramSoch | date: 2021-05-20, 07:35.