/math-c24e6038abbf5b6f85b692305939e387.png "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 /math-0cc175b9c0f1b6a831c399e269772661.png "a")
and /math-92eb5ffee6ae2fec3ad71c777531578f.png "b")
and non-centrality parameter /math-c6a6eb61fd9c6c913da73b3642ca147d.png "\lambda")
,/math-2499a3522b46ca7b3a6c6d51bea46df8.png "p(B\leq \beta )")
is defined by: 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 and and non-centrality parameter , is defined by:
/math-f3cf7ccc054b805686c44fc0f54516f0.png "P(B\leq \beta )=\sum_{j=0}^\infty e^{-\lambda /2}\frac{(\lambda /2)^j}{j!}P_b(B\leq \beta )")
where
/math-91180ecc9a0bf60887151e06c8dfe3aa.png "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.
/math-9dd4e461268c8034f5c8564e155c67a6.png "x")
(intput, double)/math-b0603860fcffe94e5b8eec59ed813421.png "\beta")
,from the beta distribution, for which /math-950fe1690089061e11454834628fd2db.png "P(B\leq \beta )")
, is to be found./math-690c394ae623b02ce772e4dc74060c48.png "0\leq x\leq 1.0")
(input, double)/math-239abc3ca0f31d28422b763a13113143.png "0<a\leq 10^6")
(input, double)/math-c861df8d5b91a81fcfe6f7b5ea282376.png "0<b\leq 10^6")
/math-945f3fc449518a73b9f5f32868db466c.png "lambda")
(input, double) , of the required beta distribution,/math-86360ed85fac3917edf68f9f48d0453c.png "0\leq lambda \leq -2.0\times \log (U)")
, where /math-4c614360da93c0a041b22e537de151eb.png "U")
is the safe range parameters as defined by NAG nag_real_safe_small_number (X02AMC). See chapter X02 in the NAG documentation./math-385e54735cbf7e164d5ca45c7419d3a9.png "prob")
(output,double)