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3.5.3.1.21 Nctcdf
Definition:
/math-ea3ac1ecdc3f1af3325d68b8b9ca1a44.png?v=0 "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 /math-4fdefba26320686bb2bd0579a0df421c.png?v=0 "\nu")
degrees of freedom and non-centrality parameter /math-77a3b715842b45e440a5bee15357ad29.png?v=0 "\delta")
,/math-257158735372a9980fb117f853b16474.png?v=0 "P(T\leq t)")
is defined by:
/math-5332bbbe5c1ee549de1eb9c6c21be58c.png?v=0 "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
/math-5c6a0eb6b719d0dad5593a2fec65b12c.png?v=0 "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 degrees of freedom, t.
/math-de517204172b6449627263b307959bbf.png?v=0 "-\infty <t<+\infty")
.
- df (intput,double)
- The degrees of freedom of the Student's t-distribution,.
/math-73b1ce17de56349b781b400f490683a2.png?v=0 "df\geq 0")
. - delta (intput,double)
- The non-centrality parameter of the Student's t-distribution,.
- maxiter (intput,int)
- Optional. Maximum number of iterations, default value is 100.
- prob (output,double)
- The probability.