prob = ncbetacdf(x, a, b, lambda) computes the cdf with the lower tail of the non-central beta distribution. The lower tail probability for the non-central beta distribution with shape parameters a and b and non-centrality parameter \lambda ,p(B\leq \beta ) is defined by:

 P(B\leq \beta )=\sum_{j=0}^\infty e^{-\lambda /2}\frac{(\lambda /2)^j}{j!}P_b(B\leq \beta )


 P_b(B\leq \beta )=\frac{\Gamma (a+b)}{\Gamma (a)\Gamma (b)}\int_0^\beta B^{a-1}(1-B)^{b-1}dB

which is the central beta probability function or incomplete beta function.


x (intput, double)
the deviate,\beta ,from the beta distribution, for which P(B\leq \beta ) , is to be found. 0\leq x\leq 1.0
a (input, double)
the first shape parameter, a, of the required beta distribtution. 0<a\leq 10^6
b (input, double)
the second shape parameter, b, of the required beta distribtution.0<b\leq 10^6
lambda (input, double)
the non-centrality parameter,\lambda , of the required beta distribution,0\leq lambda \leq -2.0\times \log (U) , where U is the safe range parameters as defined by NAG nag_real_safe_small_number (X02AMC). See chapter X02 in the NAG documentation.
prob (output,double)
the probability.