GAMMAINV in Apple Numbers: Gamma percentiles and inverse distribution

• Introduced: Documented in Apple’s Formulas and Functions Help 15.4; the original introduction release is not established.
• Availability: Currently documented for Numbers in that help version; it is not a final supported-version endpoint.
• Scope: Shared iWork function help. Availability in individual clients and older releases is not established by this check.
• Checked: October 14, 2026, against the official GAMMAINV reference. Documentation check; not a new native test.

GAMMAINV translates a desired cumulative probability into the nonnegative measurement threshold for a specified gamma distribution. Applications include model-based service completion cutoffs, positive lifetimes and queueing-time targets, when a gamma model fits. It does not learn alpha and beta from observed data, count a table’s entries, or estimate real-world coverage without separately checking the model. Use GAMMADIST with mode 1 to evaluate a probability at a known cutoff. [A1, A2, C1]

=GAMMAINV(probability, alpha, beta)

The official signature has three arguments, all required, and Apple does not document any omitted defaults. Apple’s prose calls alpha and beta shape parameters, but the companion GAMMADIST examples and independent mathematical checks agree with alpha as shape, beta as scale. This is important: many external treatments use a rate parameter instead, and blindly copying that rate into beta changes answers. The return value is an x on the original measurement scale, not a number from 0 to 1. [A1, A2, C1]

In mathematical notation this is the gamma CDF quantile: find x such that F_gamma(x; alpha, beta) = probability. For alpha=1 (the exponential special case) the quantile simplifies to -beta × LN(1−p). This identity is independently verified and is not a claim about Numbers’ internal algorithm. [C1]

Create a Numbers table ResponseTargets, with B1 Probability, C1 Alpha, D1 Beta, and E1 Threshold x. Enter B–D data for rows 2–6 below, and place the row-2 formula into E2, filling it down. This example assumes positive minutes, alpha=2, beta=3; the parameters do not change per row, but they are written on every row so the formulas are simple and independently reproducible. [A5, C1]

The theoretical 90th-percentile target of 11.6691605096 means the model predicts a 90% chance of completion at or before that number of minutes. It is not a guarantee about measured service performance, and model percentiles are not interchangeable with arithmetic averages. [C1]

=GAMMAINV(0.8,1,2)
=GAMMAINV(0.8,2,1)

Apple reports 3.2188758248682 and 2.99430834700212, respectively. Independent quantile calculations yield 3.2188758248682 and 2.99430834700212, which agree to Apple’s display precision. These checks used SciPy, not the Numbers app. [A1, C1]

Verify the selected percentile using the gamma CDF

=GAMMADIST(GAMMAINV(0.9,2,3),2,3,1)

The mathematical expectation is 0.9, up to computational rounding. The GAMMADIST fourth argument must be 1 (cumulative), not 0 (density); otherwise it is not the inverse relationship. This is a useful internal consistency review even without a native test. [A2, C1]

Scale property for comparable time units

=GAMMAINV(0.9,2,3)
=GAMMAINV(0.9,2,6)

Independently expected 11.6691605096 and 23.3383210192: doubling beta doubles the gamma quantile when alpha and probability stay fixed. This follows from beta behaving as a scale, not a rate. [C1]

Alpha=1 special case gives a direct check

=GAMMAINV(0.8,1,2)
=-2*LN(1-0.8)

Both are mathematically 3.21887582487. This independent check also helps catch an accidental use of 80 instead of 0.8, or beta=0.5 instead of beta=2. Actual input parsing and operator acceptance are not natively tested. [C1]

Keep parameters fixed and vary p

If C2=2 and D2=3 contain the shared parameters, then to evaluate p from B3 with fixed parameters use:

=GAMMAINV(B3,$C$2,$D$2)

The dollar markers lock references when the formula is filled down. The worksheet rows above instead use local C/D parameter cells, so do not mix strategies unknowingly. In another named Numbers table, include the correct table qualifier as described below. [A5]

Why p=1 does not belong in this formula

A mathematical gamma distribution has no finite 100th percentile because the upper tail extends without bound. Thus Apple’s documented restriction p<1 is substantive, not merely a formatting quirk. Similar reasoning excludes p=0 in Apple’s syntax even though a mathematical limiting cutoff approaches zero. Do not substitute exact endpoints and assume they are valid formula arguments. [A1, C1]

Apple’s Portuguese-Brazil help calls the corresponding function INVGAMA, while English Numbers uses GAMMAINV. The localized example =INVGAMA(0,8; 1; 2) means p=0.8, alpha=1, beta=2; the semicolon separates arguments and the comma is decimal punctuation. Use the Functions Browser in the recipient’s locale to avoid paste errors. [A3]

Build each example as a Numbers table, not an assumed Excel worksheet: enter row-1 headings, type the numeric values in the listed cells, enter each formula beginning with =, and fill down only where instructed. B2 addresses a cell in the current table; copied relative references change by row. A locked reference such as $C$2 keeps a shared parameter fixed. Apple documents that a sheet can contain multiple named tables; if the source is in another table named Model, select the actual cell in the Formula Editor or use a table-qualified reference such as Model::B2. Do not assume a single global sheet grid. [A5]

For LOGINV and GAMMAINV, keep probability inputs as numeric values strictly between 0 and 1, not 90 for a 90% target. You may format cumulative probability results as Percent, but formatting does not alter a mathematical value. The LOGNORMDIST and GAMMADIST first arguments are observation thresholds, not probabilities. Keep parameters numeric and do not append units inside formula input cells. If copied formulas point to the wrong table or a moving shared parameter, inspect the reference tokens in Numbers. [A5]

Apple’s individual function help specifies permitted argument domains; it does not document a stable displayed error token for every invalid input, device, locale, or cell-type conversion. Consequently the following are predicted invalid inputs or user misunderstandings, not observed Numbers errors. No #... token or screenshot is invented. [A1, A4]

The function’s English signature and examples are from Apple Formulas and Functions Help 15.4, inspected 2026-10-13 UTC. Apple also documents formula editing and references for Numbers; the Help navigation covers Apple’s iWork formula ecosystem, but the existence of a current documentation article is not proof of native execution on Mac, iPad, iPhone, iCloud, or older versions. Apple publishes app release documentation, which must not be read as evidence that this particular function debuted in that release. Its earliest supported Numbers version was not independently established. [A1, A4, A5, A6]

Do not transfer Excel, Google Sheets or other spreadsheet engines’ default arguments, error codes, statistical parameter definitions, locale punctuation, or precision guarantees to Numbers. Finite-precision corner cases, text/blank coercion, large-parameter stability, and exact error messages require native confirmation. These guides were checked against documentation and by independent numerical computation only; there was no Apple Numbers execution, import/export test, screenshot or historical-platform regression test. Intermediate expected results below are rounded for readability; a Numbers cell’s number format may show fewer digits. [A1, C1]

• GAMMAINV — authoritative signature, restrictions and both official examples. [A1]
• GAMMADIST — forward gamma CDF or density selected by the required fourth argument. [A2]
• EXP — part of gamma α=1 exponential special case. [C1]
• LN — appears in the α=1 quantile identity. [C1]

• [A1] Apple — GAMMAINV, Formulas and Functions Help 15.4, checked 2026-10-13: canonical spelling, syntax, argument order/types and domain, documented example(s), and listed see-also links.
• [A2] Apple — linked companion function, checked 2026-10-13: relationship, counterpart’s syntax and input restrictions. An independently computed inverse/CDF identity is labelled separately below.
• [A3] Apple — Portuguese (Brazil) localized function help, checked 2026-10-13: translated function spelling and region-appropriate argument/decimal punctuation. The localized identifier does not justify a separate English route.
• [A4] Apple — Types of arguments and values, checked 2026-10-13: numeric and modal argument categories; exact individual restrictions come from [A1].
• [A5] Apple — Refer to cells in formulas, checked 2026-10-13: current-table, cross-table, and fixed/relative reference conventions.
• [A6] Apple — Numbers release documentation for Mac, checked 2026-10-13: app-level changes, not proof of introduction of GAMMAINV or native confirmation.
• [C1] Independent Python SciPy 1.17.0 calculations plus elementary probability identities, executed 2026-10-13 UTC, using the displayed input cases. These are not Apple Numbers tests and not an official Apple claim.