3.5.3.2.18 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.