Notation in probability and statistics: Difference between revisions

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==Critical values==

{{Unreferenced section|date=March 2021}}

The ''&alpha;''-level upper [[critical value]] of a [[probability distribution]] is the value exceeded with probability &<math display="inline">\alpha;</math>, that is, the value ''x''<submath display="inline">''&x_\alpha;''</submath> such that ''F''(''x''<submath display="inline">''&F(x_\alpha;''</sub>) =&nbsp; 1&nbsp;&minus;&nbsp;''&-\alpha;''</math>, where ''<math display="inline">F''</math> is the cumulative distribution function. There are standard notations for the upper critical values of some commonly used distributions in statistics:

*<math display="inline">z_\alpha</math> or <math display="inline">z(\alpha)</math> for the [[standard normal distribution]]

*<math display="inline">t_{\alpha,\nu}</math> or <math display="inline">t(\alpha,\nu)</math> for the [[Student's t-distribution|''t''-distribution]] with <math display="inline">\nu</math> [[Degrees of freedom (statistics)|degrees of freedom]]