BETAINV Function (Gnumeric)

• Introduced: First release not established; this name is present in the tested Gnumeric 1.12.57 and the cited 1.12.62 source.
• Availability: Supported in Gnumeric 1.12.62 according to its function-specific registration. No retirement endpoint is established.
• Scope: Desktop Gnumeric with the fn-stat module enabled. Examples use English comma-separated formulas.
• Checked: October 14, 2026. Reference and boundary tables were recalculated by Gnumeric 1.12.57 and checked independently. The 1.12.62 contract was source-checked, not executed.

The function solves I_z(alpha,beta)=p and returns a+(b−a)z. It is an inverse CDF, not 1/BETADIST. The shapes describe the distribution on the standardized interval; they are not the arithmetic mean and standard deviation of the measurements. Official BETAINV reference.

=BETAINV(p,alpha,beta [, a [, b]])

Only the two interval bounds are optional. Brackets indicate optional arguments and are not typed. Use numeric cells or numeric inputs. The formulas use decimal points and commas; localized entry conventions require separate checks. Gnumeric 1.12.62 help and evaluator.

Enter each formula in a separate cell. The displayed references are rounded to twelve decimal places and agree with the recorded Gnumeric 1.12.57 recalculation within ordinary floating-point precision. Keep the stored result for subsequent calculations.

Put probability 0.5248 in A2, shapes 2 and 3 in B2:C2, and bounds 10 and 20 in D2:E2. Enter =BETAINV(A2,B2,C2,D2,E2) in F2. The result is 14. In G2, =BETADIST(F2,B2,C2,D2,E2) should recover 0.5248.

Keep the same shapes and bounds on both sides. Format the probability separately from the cutoff, and retain F2’s full precision rather than copying a rounded display into the check.

Construct percentile bounds

For a central 80% interval, use probabilities 0.1 and 0.9, leaving 10% in each tail. =BETAINV(0.1,2,3) and =BETAINV(0.9,2,3) produce the two cutoffs shown in the table. Their cumulative probabilities differ by 0.8, although the physical interval need not occupy 80% of the scale.

An affine change of bounds preserves percentiles: =BETAINV(0.5,2,3,10,20) equals =10+10*BETAINV(0.5,2,3). This is a useful unit-conversion check. It does not mean the median is the midpoint of an asymmetric beta model.

The implemented domain includes p=0 and p=1, which return a and b. Probabilities outside [0,1], nonpositive shapes and a≥b produce #NUM!. This finite-endpoint behavior differs from unbounded normal or F quantiles. Alpha and beta are shape parameters even though the short help labels them as scale parameters.

The following are observed cell results from the same 1.12.57 command-line recalculation. F5 was genuinely empty. A blank is not necessarily an omitted argument or a valid observation, so validate required data instead of treating every defaulted zero as intentional.

The fixtures do not certify every locale, extreme tail, imported type or newer binary build. The current wrapper agrees with the documented argument contract; shared numerical helpers can change between releases.

• BETADIST
• BETA.DIST
• BETAINV official manual entry
• Version-pinned argument contract and calculation