TDIST

What it does

TDIST(x, deg_freedom, tails)

TDIST(x,deg_freedom,tails) returns a Student-t upper-tail probability. One tail means P(T>x); two means P(abs(T)>x). The compatibility function takes nonnegative x, not a signed cumulative-probability argument.

Try it

=TDIST(1,1,2) is about 0.5; with one tail it is about 0.25. At one degree of freedom the distribution is Cauchy, giving this useful control.

Quirks

Degrees of freedom and tails are truncated. Degrees below one, negative x and tails other than one or two give #NUM!; nonnumeric inputs give #VALUE!. Halving or doubling a tail is a different operation from changing a CDF into an upper tail.

How to implement

For nonnegative x and degree v, form t2=x*x, den=v+t2, and the paired beta arguments z=v/den, zc=t2/den. The current two-tail route evaluates the beta ratio with shape v/2 and 1/2 using both supplied arguments; the one-tail route halves that result. Computing zc=1-z can lose an observed rounding. At x=v=1 both beta arguments are one half and the two-tail result is one half. Inner beta-ratio last bits remain open.

Rust code

43 tdist "TDIST" (3, 3) [V "x", V "deg_freedom", V "tails"] |s, a, sv| {
    let [x, df, tails] = nums::<3>(s, a)?;
    out(
        s,
        match tails.trunc() as i32 {
            1 => cft::t_dist_rt_kernel(x, df),
            2 => cft::t_dist_2t_kernel(x, df),
            _ => Err(WorksheetErrorCode::Num),
        },
    )
}

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

T.DIST.RT and T.DIST.2T make the tail explicit; T.DIST provides a signed CDF/density; TINV finds a two-tail critical value.

Named variants

No named variants are recorded yet.