StatsNCFPDF

StatsNCFPDF (x, n1, n2, d)

The StatsNCFPDF function returns the probability distribution function of the noncentral F distribution.

$$\displaystyle f\left(x ; n_{1}, n_{2}, d\right)=\frac{\exp (-d / 2)}{B\left(\frac{n_{1}}{2}, \frac{n_{2}}{2}\right)} x^{n_{1} / 2-1}\left(x n_{1}+n_{2}\right)^{-\left(n_{1}+n_{2}\right) / 2} n_{1}^{n_{1} / 2} n_{2}^{n_{2} / 2}{ }_{1} F_{1}\left(\frac{n_{1}+n_{2}}{2}, \frac{n_{1}}{2}, \frac{x d n_{1}}{2\left(x n_{1}+n_{2}\right)}\right),$$

where B() is the beta function and ₁F₁() is the hypergeometric function HyperG1F1.

References

Abramowitz, M., and I.A. Stegun, "Handbook of Mathematical Functions", 446 pp., Dover, New York, 1972.

Evans, M., N. Hastings, and B. Peacock, Statistical Distributions, 3rd ed., Wiley, New York, 2000.

See Also

Statistical Analysis, StatsNCFCDF, StatsInvNCFCDF