BETADIST Function (Calligra Sheets)

• Introduced: First release not established; the name is present in Calligra 2.4.0 source.
• Supported in: Calligra Sheets 26.08.2, with no retirement established.
• Scope: Desktop Sheets with the Statistical module. Examples use English semicolon-separated formulas.
• Checked: October 14, 2026. Selected formulas ran through the official 25.04.2 engine library. Source and independent mathematics were checked. This is engine evidence, with no GUI-cell or import verification; 26.08.2 was source-checked only.

BETADIST defaults to the cumulative beta probability on an interval. With shapes alpha and beta and lower/upper bounds L and U, the scaled argument is t=(x−L)/(U−L). For valid positive shapes and L<U, the cumulative result is the regularized incomplete beta integral at t. The optional sixth argument selects the density branch, whose implementation has the warning above. Function help.

=BETADIST(x;alpha;beta[;lower[;upper[;cumulative]]])

Three arguments are required. Lower defaults to 0, upper to 1 and cumulative to TRUE. The cumulative flag is converted to an integer, so a fractional value below 1 can select the zero/density branch. Use an explicit TRUE or FALSE and valid numeric inputs. The ordinary mathematical model requires alpha>0, beta>0 and lower<upper. Brackets indicate optional arguments and are not entered in the formula. Registration and implementation.

The engine and mathematical columns are separate. Results are rounded to twelve decimal places, or thirteen significant digits in scientific notation for very small or large values. This is a display choice, not an accuracy guarantee. NaN and infinity are nonfinite outputs; an engine error flag is checked separately from those values.

For a beta model with shapes 2 and 3 on [0,1], the exact cumulative probability at 0.5 is 0.6875. This can describe the fraction of a modeled bounded quantity below a cutoff. On [10,14], x=12 maps to the same t=0.5 and therefore has the same cumulative probability.

The density is different: the correctly normalized density is t^(alpha−1)(1−t)^(beta−1) divided by B(alpha,beta)(U−L). At x=0.5 with shapes 2 and 3 on [0,1], it is 1.5. A density can exceed 1; only its integral over an interval is a probability.

The source forms B(alpha,beta) from gamma functions and multiplies by it instead of dividing. It also omits division by U−L. For shapes 2 and 3, B=1/12, so the tested unit-interval density is approximately 1/96 rather than 1.5, a factor of 144. The displayed advanced check multiplies that one diagnostic by 144 and returns about 1.500000000160.

That factor is specific to these shapes and this interval; it is not a general repair formula. On [10,14], the correct midpoint density is 0.375 but the same source branch still produces about 0.010416666668. For a uniform beta model on that interval, the correct density is 0.25 rather than the engine’s approximately 1.

The executed advanced check was:

=BETADIST(0.5;2;3;0;1;0)*144

Its engine result was 1.50000000016.

The source returns zero for x below lower, nonpositive shapes or equal bounds, rather than flagging all those invalid parameters. Above upper it returns 1 for cumulative and 0 for density. Reversed bounds also need explicit validation. Endpoint densities with shapes below 1 yielded positive infinity with a false engine error flag. That is a nonfinite result, not an ordinary finite probability or GUI error display.

• Function-specific implementation
• Versioned function help
• Beta helper
• Gamma helper
• Conversion helper
• Gamma approximation coefficients

The statistical module and value-calculation helpers are byte-identical between the inspected 25.04.2 and 26.08.2 sources. That comparison supports the source discussion but does not establish later-version native output, every locale or arbitrary extreme-parameter accuracy.

NORMDIST.