# ncfinv

Noncentral F inverse cumulative distribution function

## 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 `NU1`, denominator degrees of freedom `NU2`, and positive noncentrality parameter `DELTA` for the corresponding probabilities in `P`. `P`, `NU1`, `NU2`, and `DELTA` can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of `X`. A scalar input for `P`, `NU1`, `NU2`, or `DELTA` is expanded to a constant array with the same dimensions as the other inputs.

## Examples

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 that computed 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```

If the true ratio of variances is 2, what is the typical (median) value you would expect for the F statistic?

```ncfinv(0.5,5,20,2) ans = 1.2786 ```

## References

 Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. Hoboken, NJ: Wiley-Interscience, 2000.

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