F.DIST.RT

What it does

F.DIST.RT(x, deg_freedom1, deg_freedom2)

F.DIST.RT(x, deg_freedom1, deg_freedom2) returns an F-distribution right-tail probability. The first degree count belongs to the numerator and the second to the denominator.

Try it

=F.DIST.RT(3,2,2) is about 0.25. With both degree counts two, the mathematical left CDF is x/(1+x) and the right tail is 1/(1+x).

Quirks

Degree counts are truncated. Microsoft documents #VALUE! for nonnumeric arguments and #NUM! for negative x or degree counts below one. The current shared helper also rejects a nonfinite x and a truncated degree count above 10^10; that code cap is separate from the opened page’s lower-bound wording.

The left CDF rises from zero and the right tail falls from one. The density option in F.DIST is a third quantity, rather than either of those probabilities. At x=0 the current density gives #NUM! for numerator degree one, one for degree two and zero for higher degrees. Those density cases do not change the endpoint probabilities.

The current beta transformation forms the product of x and numerator degrees directly. Extreme products or beta/gamma approximations need their own numerical error and publication checks; a finite mathematical probability alone does not ensure this candidate evaluates it successfully.

How to implement

The current right-tail route evaluates a lower beta ratio after swapping the degree roles. Use ordinary binary64 stores D.

1. Validate finite nonnegative x and the truncated positive degree counts d1 and d2.
2. Calculate num=D(d1*x) and den=D(d2+num).
3. Independently store z=D(d2/den) and w=D(num/den). Pass both to bratio(d2/2,d1/2,z,w) and return its first, lower-ratio result. The explicit complement w is part of the current argument construction.
4. Apply worksheet number publication, preserving the host’s error/refusal distinction.

With d1=d2=2 and x=3, num is six and den eight. The transformed beta shapes are one and one, a uniform distribution, so z=2/8 gives the right probability one quarter. The companion left route uses 6/8 instead.

Do not obtain this tail by subtracting a rounded left CDF from one. A separately scaled ratio can avoid overflowing d1*x in a mathematical implementation, but changes the current computation tree. The paired-argument wrapper is more specific than a generic beta identity; the inner beta approximation and remaining recorded mismatches still prevent a whole-domain identification.

Rust code

31 f_dist_rt "F.DIST.RT" (3, 3) [V "x", V "deg_freedom1", V "deg_freedom2"] |s, a, sv| {
    let [x, d1, d2] = nums::<3>(s, a)?;
    out(s, cft::f_dist_rt_kernel(x, d1, d2))
}

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

F.INV.RT maps an upper-tail probability to a critical value. F.DIST provides the left CDF or density; F.TEST starts with two samples.

Named variants

No named variants are recorded yet.