BETADIST Function (Gnumeric)

• Introduced: Gnumeric 0.25, explicitly listed among the new functions in its release notes.
• 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.

For z=(x−a)/(b−a), the result is the regularized beta integral I_z(alpha,beta). On the standard interval, the density is proportional to z^(alpha−1)(1−z)^(beta−1). Although the help labels alpha and beta as scale parameters, they are the two shape parameters; the bounds supply the measurement scale. Official BETADIST reference.

=BETADIST(x,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 threshold 0.5 in A2, shape 2 in B2 and shape 3 in C2. In D2 enter =BETADIST(A2,B2,C2), which gives 0.6875. This is the probability at or below 0.5, not a density of 0.6875 at that exact point. The complementary probability above 0.5 is =1-D2, or 0.3125.

Label B2 and C2 as shapes rather than observed mean and standard deviation. With alpha=2 and beta=3, the standard-interval mean is alpha/(alpha+beta)=0.4; entering 0.4 as alpha would specify a different model.

Change the measurement interval

Suppose the modeled quantity ranges from 10 to 20. =BETADIST(14,2,3,10,20) evaluates the same standardized point as =BETADIST(0.4,2,3) and gives 0.5248. Standardize the threshold together with the bounds; changing only x changes the probability.

For a central band, subtract two cumulative values with identical shapes and bounds. =BETADIST(0.8,2,3)-BETADIST(0.2,2,3) gives 0.792. A probability over an interval is a difference of CDFs, not a difference of beta-density heights.

The release rejects x outside [a,b], nonpositive shapes and a≥b with #NUM!. The endpoints themselves are valid: x=a returns 0 and x=b returns 1. There is no optional cumulative argument in this spelling; use the separately documented BETA.DIST contract if a density is needed. Bounds may be negative, provided a<b and x lies inside them.

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.

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