GAMMA.INV

What it does

GAMMA.INV(probability, alpha, beta)

GAMMA.INV(probability,alpha,beta) returns a gamma-distribution quantile for positive shape alpha and positive scale beta. It seeks the x whose lower cumulative probability is the requested p. Beta scales x’s units, rather than supplying an exponential rate.

Try it

=GAMMA.INV(0.5,1,2) is about 1.3862943611. The mathematical shape-one CDF is 1-exp(-x/2), so its median solves x=-2*ln(0.5).

=GAMMA.INV(0.5,1,4) is about 2.7725887222. Doubling the scale doubles the mathematical quantile, though the current search has its own stored path.

Quirks

Microsoft documents #VALUE! for a text argument, #NUM! for nonpositive shape or scale and for p outside zero to one. The current helper returns zero at p=0 and #NUM! at p=1, where there is no finite mathematical gamma quantile.

The opened modern page documents an iterative search limit of 64 tries followed by #N/A; the legacy GAMMAINV page describes 100 tries. This documentation difference is not a measured change between named Excel builds, and the current helper uses its own bracket and adjacent-value search.

The current inverse callback is the generic lower gamma ratio. It does not call the public GAMMA.DIST wrapper, whose half-shape and shape-one cases have separate ERF and exponential paths.

How to implement

1. Validate finite positive alpha and beta and finite p. Return zero for p=0; reject p<0 or p>=1 under the current endpoint rule.
2. With ordinary binary64 operations, initialize lo=0 and hi=beta*max(alpha+10*sqrt(alpha)+10,1).
3. Evaluate F(x)=regularized_gamma_p(alpha,D(x/beta)). While F(hi) is below p, double hi. The current source permits 200 expansion checks; extreme-parameter bracketing and nonfinite callbacks remain explicit limitations.
4. Bisect the nonnegative binary64 encodings of lo and hi, as in the shared ordered-value inverse recipe. If F(mid)>=p keep the midpoint as the upper endpoint; otherwise keep it as lower. Return the upper value when the endpoint encodings are adjacent.
5. Apply worksheet numeric publication. The candidate searches x on its scaled interval; it does not simply solve once at scale one and multiply an already rounded answer by beta.

For alpha=1, beta=2 and p=0.5, the mathematical equation gives about 1.38629436111989. That explains the example. Its numerical candidate still depends on the generic forward callback and upper-adjacent return, rather than an exact inverse exponential formula.

A bracketed Newton method or a residual-based stopping rule is another reasonable mathematical solver. Changing the callback to the public CDF’s special branches is also a separate numerical candidate. Forward-ratio errors, conditioning in the tails, bracket extremes and remaining inverse mismatches remain open; no whole-function Handbook suite is published.

Rust code

56 gamma_inv "GAMMA.INV" (3, 3) [V "probability", V "alpha", V "beta"] |s, a, sv| {
    let [p, alpha, beta] = nums::<3>(s, a)?;
    out(s, bg::gamma_inv_kernel(p, alpha, beta))
}

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

GAMMA.DIST supplies the forward distribution. GAMMAINV is the compatibility spelling. CHISQ.INV uses gamma shape df/2 and scale two; BETA.INV inverts a bounded distribution.

Named variants

No named variants are recorded yet.