BETADIST in WPS Spreadsheet: Beta Cumulative Probability
Evaluate a beta cumulative distribution with explicit bounds, derive simple polynomial cases and distinguish cumulative probability from density.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
BETADIST returns a beta cumulative probability: the probability up to a specified x under the chosen beta model. The WPS narrative sometimes combines the words “cumulative” and “density,” but its formal description and worked example establish a cumulative distribution function. The documented legacy signature has no TRUE/FALSE mode selector.
Syntax and source cautions
=BETADIST(x, alpha, beta, [A], [B])
Alpha and beta are positive shape parameters. A and B are interval bounds. WPS describes default bounds 0 and 1 when bounds are omitted. All original formulas here supply both bounds explicitly as 0 and 1 and use x strictly inside the interval.
The page prints the nonnumeric-input error as #VALVE!. That spelling is not treated here as a verified error token or silently replaced with another product’s behavior. Exact invalid-input results, omitted-bound combinations and endpoint handling remain outside the original controls. No BETA.DIST alias or density argument is assumed.
Original polynomial example
For alpha = beta = 2 on [0,1], the beta density is 6x(1−x), so integrating from 0 to x gives the cumulative polynomial 3*x^2 − 2*x^3.
- Enter 0.25, 2, 2, 0 and 1 in B1:B5.
- Use
=BETADIST(B1,B2,B3,B4,B5)in B7. - Independently calculate 3*(0.25)^2 − 2*(0.25)^3 = 0.15625.
This is the probability of a model value at or below 0.25, not the density at that point. The density there is 1.125, a different quantity with a different interpretation.
Independently checkable cases
| Formula | Cumulative polynomial | Expected probability |
|---|---|---|
=BETADIST(0.25,1,1,0,1) |
x | 0.25 |
=BETADIST(0.75,1,1,0,1) |
x | 0.75 |
=BETADIST(0.25,2,1,0,1) |
x squared | 0.0625 |
=BETADIST(0.75,1,2,0,1) |
2x − x squared | 0.9375 |
=BETADIST(0.25,2,2,0,1) |
3x squared − 2x cubed | 0.15625 |
=BETADIST(0.5,2,2,0,1) |
3x squared − 2x cubed | 0.5 |
The uniform case alpha = beta = 1 is a useful reference. Different shape parameters change the model, even when x and the interval remain the same.
Advanced interval and symmetry checks
For the symmetric beta(2,2) model, the CDF at 0.75 is 0.84375. The probability between 0.25 and 0.75 is therefore 0.84375 − 0.15625 = 0.6875. The two endpoint CDFs add to one by symmetry.
These calculations describe a continuous model on a bounded interval. A proportion being between zero and one does not by itself justify choosing a beta distribution or its parameters. Do not substitute a normal distribution merely because the default interval is [0,1].
Vendor example and numerical scope
The official walkthrough uses x = 4, alpha = 9, beta = 10, A = 1 and B = 5, displaying 0.994578221. The example supports its cumulative interpretation on a shifted interval. The original controls remain on explicit [0,1] bounds, with elementary independent formulas rather than a general numerical beta implementation.
The lesson discusses nonpositive shape parameters and invalid bounds, but no malformed-input token is asserted as an observed result here. Very small tail probabilities, extreme shapes and implementation precision need separate validation. PROB concerns a finite discrete probability table, not this continuous model.
Availability and evidence scope
The official WPS lesson is dated 2019-06-17 and does not specify its applicability edition or platform. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.
The complete lesson and its formula images and walkthrough were inspected on October 18, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.