/math-b0cc8758246ccfac73880811dffd3685.png "prob = ncfcdf(f, df1, df2, lambda)")
computes the probability associated with the lower tail of the non-central /math-bf64ba6aa4c2d7bb776f5b41188a0c1b.png "\digamma")
or variance-ratio distribution.
computes the probability associated with the lower tail of the non-central or variance-ratio distribution.
The lower tail probability of the non-central F-distribution with /math-69c6c7d65b5d5962975b353743338da8.png "\nu _1")
and /math-5cc876f94cb2e07c0316e43816cc7450.png "\nu _2")
degrees of freedom and non-centrality parameter /math-c6a6eb61fd9c6c913da73b3642ca147d.png "\lambda")
,
/math-d6ed1cd77819a39c55652937f4800952.png "P(\digamma \leq f)")
is defined by:
=/math-d0d2b6bcf9faa07dc7870b0af5189244.png "\int_\lambda ^f P(\digamma )d\digamma")
,
Where
/math-b18b727978febc94496b2575dec1471c.png "P(\digamma )=\sum_{j=0}^\infty e^{-\lambda /2}\frac{(\lambda /2)^j}{j!}\times\frac{(\nu _1+2j)^{(\nu _1+2j)/2}\nu _2^{\nu _2/2}}{B((\nu _1+2j)/2,\nu _2/2)}\times")
![u^{(\nu _1+2j-2)/2}\left[ \nu _2+(\nu _1+2j)u\right] ^{-(\nu _1+2j+\nu _2)/2}](../images/Ncfcdf_(function)/math-795e99d1f78eea1daee1fdc4ebaadbf7.png "u^{(\nu _1+2j-2)/2}\left[ \nu _2+(\nu _1+2j)u\right] ^{-(\nu _1+2j+\nu _2)/2}")
and /math-700bfedf457b9ae1ceeda15ddd304a7e.png "B\left( \cdot ,\cdot \right)")
is the beta function.
/math-493e0e5234ce86ea0c7a30b6005588cf.png "f{>}0")
.. /math-127f3f17669fc4bd4d3107c9a6e34cc3.png "0<df1\leq 1.0e6")
.. /math-5018dbca62ef3ca6ffcb84164c59aaac.png "df2>0.")
/math-945f3fc449518a73b9f5f32868db466c.png "lambda")
, of the required beta distribution,/math-3382998cfcda553bb400bd0a334bcf4e.png "0\leq lambda\leq -2.0\times \log \left( U\right) ,")
where U is the safe range parameters as defined by by NAG nag_real_safe_small_number (X02AMC). See chapter X02 in the NAG documentation.