PlanMaker GAMMA.INV Function: Find gamma quantiles with scale parameters

=GAMMA.INV(Probability, Alpha, Beta)
=GAMMAINV(Probability, Alpha, Beta)

All three arguments are required. Probability is the left-tail cumulative area. Alpha and Beta must be positive. The short help calls both shape parameters; the independent model used here distinguishes dimensionless shape Alpha from scale Beta, which has the same units as the returned quantile.

If another source supplies a gamma rate λ, the scale is 1/λ. Do not enter the rate unchanged in the Beta position. For a finite positive quantile, use an interior probability 0<p<1; exact endpoint handling is an application question rather than something established by inclusive 0 to 1 wording alone.

Enter 0.95 in B2, 1 in B3, and 2 in B4. In B6 enter =GAMMA.INV(B2,B3,B4).

When Alpha=1, the gamma model is exponential with scale Beta. Its CDF is 1−exp(−x/Beta), so solving for x gives −Beta×LN(1−p).

The first two are −2×LN(0.5) and −2×LN(0.05). The third uses the shape 2/scale 2 identity CDF(4)=1−3×exp(−2). Paired GAMMAINV median and 95th-percentile calls check the documented alias without assuming identical behavior merely from similar names.

The official reference describes an iterative inverse with up to 100 iterations. If no result is found within approximately ±3×10⁻⁷ of Probability, it documents #N/A and cancellation of the approximation.

This measures the CDF residual at the returned quantile. It does not establish an absolute x tolerance of 3×10⁻⁷ or near-machine-precision agreement with a reference quantile. Scale and local density influence how probability error translates into an x difference.

For a practical native round-trip check, enter:

=GAMMA.DIST(GAMMA.INV(0.95,1,2),1,2,TRUE)

The target is 0.95. For this shape 1 example, independently compute 1−exp(−x/2) from the raw returned x as a separate check. A native forward/inverse pair alone can share numerical limitations. Do not round x before calculating its residual.

For shape 1 and scale 2, the mathematical median is about 1.3863 while the 95th percentile is about 5.9915. These are model thresholds with different cumulative areas, not an estimate and an error bound around it.

Doubling the scale from 2 to 4 doubles every mathematical quantile while leaving Alpha and Probability unchanged. This scaling relation helps catch a mistaken rate-versus-scale entry. The shape 1 mean is 2, which is neither its median nor its 95th percentile.

A percentile describes the specified distribution of an individual modeled variable. It is not automatically a confidence bound for an estimated mean, a service guarantee, or a prediction that a particular event occurs before the threshold. The function does not estimate Alpha or Beta from observations.

Probability 0 has a limiting gamma quantile of 0, while probability 1 has an unbounded upper quantile. The tested endpoint results are not exact mathematical quantiles: =GAMMA.INV(0,1,2) returns approximately 1.49011611938477×10⁻⁷, while =GAMMA.INV(1,1,2) returns 5,000,000 in this build. The latter is a finite application result, not a valid finite 100th percentile of an unbounded gamma model and not a value to interpret as an upper guarantee. Use interior probabilities and check residuals. The zero-scale call =GAMMA.INV(0.5,1,0) returns #NUM!.

The documented #N/A iterative failure is different from invalid-input errors. Do not assume every unsupported value produces #N/A, and do not turn a failure into a finite percentile without understanding why it occurred.

Very small probabilities, extreme shapes, and huge scales can be numerically demanding. The moderate closed-form controls do not establish convergence or precision for every valid input.

The official GAMMAINV page describes GAMMA.INV as identical, without declaring the old name deprecated or retired.

GAMMA.DIST is the forward cumulative or density function. LN and EXP express the independent shape 1 check. Follow the numeric and argument separators used by your installed locale.

The native shape 1/scale 2 median is approximately 1.38629451394081, and the 0.95 quantile approximately 5.99146440625191. GAMMAINV returns the same saved values. The shape 2 control returns approximately 3.99999991059303, displayed as 4. Independent gamma-CDF residuals at the raw quantiles meet the documented 3×10⁻⁷ probability criterion; the native 0.95 round trip is approximately 0.949999996478598.

FreeOffice PlanMaker 2024 rev F1238.1005: selected cell J2 contains =GAMMA.INV(0.5,1,2) and displays 1.38629. Raw saved values retain more digits; rounded display values are not asserted as exact mathematical equality.

Official FreeOffice PlanMaker 2024 references checked October 18, 2026: reference 1, reference 2. The first introduction release is unknown from these references. Current documentation does not imply retirement or identical behavior in every other edition.

The 9 selected formula cells for this function were tested on October 18, 2026 in FreeOffice PlanMaker 2024 rev F1238.1005, 64-bit, then saved in PMDX format and reopened with calculation meaning preserved. Paired legacy calls were included. Native observations remain distinct from independent mathematical references, teaching layouts, and advanced examples not individually executed. The proprietary implementation has not been inspected; the bounded results do not establish every tail, parameter, input type, edition, or export behavior.