3.5.3.1.21 Nctcdf

Definition:

$prob = nctcdf( t, df, delta, maxiter)$ computes the lower tail probability for the non-central Student's t-distribution.

The lower tail probability of the non-central Student's t-distribution with $\nu$ degrees of freedom and non-centrality parameter $\delta$ , $P(T\leq t)$ is defined by: $P(T\leq t)=C_\nu \int_0^\infty (\frac 1{\sqrt{2\pi }}\int_{-\infty }^{\alpha u-\delta }e^{-x^2}dx)u^{v-1}e^{-u^2/2}du,\nu >0$
with

$C_\nu =\frac 1{\Gamma (\frac 12\nu )2^{(\nu -2)/2}},\alpha =\frac t{\sqrt{\nu }}$

Parameters:

t (intput,double): The deviate from the Student's t-distribution with $\nu$ degrees of freedom, t.

$-\infty <t<+\infty$ .

df (intput,double): The degrees of freedom of the Student's t-distribution, $\nu$ . $df\geq 0$ .
delta (intput,double): The non-centrality parameter of the Student's t-distribution, $\delta$ .
maxiter (intput,int): Optional. Maximum number of iterations, default value is 100.
prob (output,double): The probability.

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Cumulative Distribution Functions (CDF)

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