alpha : float or list; the level of significance

parameter1 : list; list of parameter values

parameter2 : list; list of parameter values

noheaders : truefalse; specifies if column and row header information is included. By default this is set to false.

output : identical( matrix, embed ); controls the output of the resulting matrix. If output = embed, then a datatable component containing the matrix of values is returned. By default, output is set to matrix, and a matrix is returned.

For $x<0$ values of $F\left(x\right)$ can be obtained from $F\left(-x\right)=1-F\left(x\right)$. The values in the critical t-distribution table can be found by solving the equation $\mathrm{\alpha }$ = CDF for the t-distribution for x:

The CriticalTable command returns the critical table of values as a matrix. If embed = true, then a datatable component containing the matrix of values is returned.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Statistics}\right)\&colon;$

$\mathrm{CDF}\left(\mathrm{StudentTRandomVariable}\left(\mathrm{\&nu;}\right)\&comma;x\right)$

$\frac{1}{2}+\frac{x\mathrm{\Gamma }\left(\frac{\mathrm{\nu }}{2}+\frac{1}{2}\right)\mathrm{hypergeom}\left(\left[\frac{1}{2}\&comma;\frac{\mathrm{\nu }}{2}+\frac{1}{2}\right]\&comma;\left[\frac{3}{2}\right]\&comma;-\frac{x^2}{\mathrm{\nu }}\right)}{\sqrt{\mathrm{\pi }\mathrm{\nu }}\mathrm{\Gamma }\left(\frac{\mathrm{\nu }}{2}\right)}$

$\mathrm{fsolve}\left(0.95\&equals;\frac{1}{2}\&plus;\frac{x\mathrm{GAMMA}\left(\frac{1\cdot 2}{2}\&plus;\frac{1}{2}\right)\mathrm{hypergeom}\left(\left[\frac{1}{2}\&comma;\frac{1\cdot 2}{2}\&plus;\frac{1}{2}\right]\&comma;\left[\frac{3}{2}\right]\&comma;-\frac{x^2}{2}\right)}{\sqrt{\mathrm{Pi}\cdot 2}\mathrm{GAMMA}\left(\frac{1\cdot 2}{2}\right)}\&comma;x\right)$

$2.919985580$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{StudentT}\&apos;\&comma;\mathrm{\&alpha;}\&equals;0.95\&comma;\mathrm{parameter1}\&equals;\left[2\right]\&comma;\mathrm{noheaders}\right)$

$\left[\begin{array}{c}2.919985580353724\end{array}\right]$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{StudentT}\&apos;\&comma;\mathrm{\&alpha;}\&equals;0.80\&comma;\mathrm{parameter1}\&equals;\left[100\right]\right)$

$\left[\begin{array}{cc}\mathrm{\&nu;}& 0.80\\ 100.& 0.8452304244914336\end{array}\right]$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{StudentT}\&apos;\&comma;\mathrm{\&alpha;}\&equals;\left[0.95\&comma;0.99\right]\&comma;\mathrm{parameter1}\&equals;\left[\mathrm{seq}\left(1..10\right)\right]\right)$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{StudentT}\&apos;\right)$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{ChiSquare}\&apos;\&comma;\mathrm{\&alpha;}\&equals;0.95\right)$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{FRatio}\&apos;\&comma;\mathrm{\&alpha;}\&equals;0.975\&comma;\mathrm{parameter1}\&equals;\left[\mathrm{seq}\left(1..5\right)\right]\&comma;\mathrm{parameter2}\&equals;\left[\mathrm{seq}\left(1..2\right)\right]\&comma;\mathrm{noheaders}\right)$

$\left[\begin{array}{ccccc}647.7890114778661& 799.500000000017& 864.1629721634926& 899.5833101778674& 921.8479032996742\\ 38.506329113924004& 38.999999999999964& 39.16549456401377& 39.24841765813142& 39.298227775403205\end{array}\right]$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{Gamma}\&apos;\&comma;\mathrm{\&alpha;}\&equals;0.95\&comma;\mathrm{parameter1}\&equals;\left[\mathrm{seq}\left(1..5\right)\right]\&comma;\mathrm{parameter2}\&equals;\left[1\&comma;2\right]\right)$

$\left[\begin{array}{cccccc}\mathrm{c\backslash b}& 1.& 2.& 3.& 4.& 5.\\ 1.& 2.9957322735539895& 5.991464547107979& 8.987196820661968& 11.982929094215958& 14.978661367769948\\ 2.& 4.743864518390578& 9.487729036781156& 14.231593555171735& 18.97545807356231& 23.71932259195289\end{array}\right]$

$\mathrm{CriticalTable}\left(\&apos;\mathrm{Gamma}\&apos;\&comma;\mathrm{\&alpha;}\&equals;0.975\&comma;\mathrm{output}\&equals;\mathrm{embed}\right)$

$\mathrm{DT}$

The Student[Statistics][CriticalTable] command was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.