Editing Student's t-distribution (section)

===In general===

* The [[noncentral t-distribution|noncentral {{mvar|t}}&nbsp;distribution]] generalizes the {{mvar|t}}&nbsp;distribution to include a noncentrality parameter. Unlike the nonstandardized {{mvar|t}}&nbsp;distributions, the noncentral distributions are not symmetric (the median is not the same as the mode).
* The ''discrete Student's {{mvar|t}}&nbsp;distribution'' is defined by its [[probability mass function]] at ''r'' being proportional to:<ref>{{cite book |title=Families of Frequency Distributions |vauthors=Ord JK |publisher=Griffin |year=1972 |isbn=9780852641378 | location=London, UK |at=Table&nbsp;5.1 }}</ref> <math display="block"> \prod_{j=1}^k \frac{1}{(r+j+a)^2+b^2}  \quad \quad r=\ldots, -1, 0, 1, \ldots ~.</math> Here ''a'', ''b'', and ''k'' are parameters. This distribution arises from the construction of a system of discrete distributions similar to that of the [[Pearson distribution]]s for continuous distributions.<ref>{{Cite book |title=Families of frequency distributions |vauthors=Ord JK |publisher=Griffin |year=1972 |isbn=9780852641378 |location=London, UK |at=Chapter&nbsp;5}}</ref>
* One can generate Student {{nobr| {{math|''A''(''t'' {{!}} ''ν'')}} }} samples by taking the ratio of variables from the normal distribution and the square-root of the {{nobr|{{math|''χ''²}} ''distribution''}}. If we use instead of the normal distribution, e.g., the [[Irwin–Hall distribution]], we obtain over-all a symmetric 4&nbsp;parameter distribution, which includes the normal, the [[uniform distribution (continuous)|uniform]], the [[triangular distribution|triangular]], the Student&nbsp;{{mvar|t}} and the [[Cauchy distribution]]. This is also more flexible than some other symmetric generalizations of the normal distribution.
* {{mvar|t}}&nbsp;distribution is an instance of [[ratio distributions]].
* The square of a random variable distributed  {{math|''t''{{sub|''n''}}}} is distributed as [[Snedecor's F distribution]] {{math|''F''{{sub|1,''n''}}}}.