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# invF()

Usage:
 ```invF(P, df1, df2 [,upper:T or lower:F]), P, df1 and df2 REAL, elements of P between 0 and 1, those of df1 and df2 > 0 ```

Keywords: probabilities, random numbers, confidence intervals
```invF(p,df1,df2) computes the pth quantile (probability point, critical
value) of the F distribution with df1 and df2 degrees of freedom.

The elements of p must be between 0 and 1 and the elements of df1 and
df2 must be positive REAL numbers (not necessarily integers).

If p, df1, and df2 are not all scalars (single numbers), all non-scalar
arguments must have the same size and shape.  Any scalar arguments are
used to compute all elements of the result.

invF(p,df1,df2,upper:T) and invF(p,df1,df2,lower:F) compute the pth
upper tail quantile.  The result is mathematically equivalent to invF(1
- p, df1,df2) but may be more accurate for small p.

invF() is the inverse of cumF().

If S1sq and S2sq are sample variances from independent normal random
samples of sizes n1 and n2,, you can compute a 1 - alpha confidence
interval for the variance Var1/Var2 as
(S1sq/S2sq)/invF(vector(1-alpha/2, alpha/2), n1-1, n2-1).

invF(runi(n), df1, df2) will generate a random sample of size n from a F
distribution.

```

Gary Oehlert 2003-01-15