ncfinv (Statistics Toolbox)

Inverse of the noncentral F cumulative distribution function (cdf).

Syntax

X = ncfinv(P,NU1,NU2,DELTA)

Description

X = ncfinv(P,NU1,NU2,DELTA) returns the inverse of the noncentral F cdf with numerator degrees of freedom (df), NU1, denominator df, NU2, and positive noncentrality parameter, DELTA, for the probabilities, P.

The size of X is the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs.

Example

One hypothesis test for comparing two sample variances is to take their ratio and compare it to an F distribution. If the numerator and denominator degrees of freedom are 5 and 20 respectively then you reject the hypothesis that the first variance is equal to the second variance if their ratio is less than below:

critical = finv(0.95,5,20)

critical =

    2.7109

Suppose the truth is that the first variance is twice as big as the second variance. How likely is it that you would detect this difference?

prob = 1 - ncfcdf(critical,5,20,2)

prob =

    0.1297

References

Evans, M., N. Hastings, and B. Peacock, Statistical Distributions, Second Edition, John Wiley and Sons, 1993. p. 102-105.

Johnson, N., and S. Kotz, Distributions in Statistics: Continuous Univariate Distributions-2, John Wiley and Sons, 1970. pp. 189-200.