BETAINV in WPS Spreadsheet: Inverse Beta Quantiles

=BETAINV(probability, alpha, beta, [A], [B])

Alpha and beta are positive shape parameters; A and B define the x interval. The WPS lesson documents default bounds 0 and 1. Original formulas supply explicit 0 and 1 bounds and strictly interior probabilities, with positive shapes.

The article’s nonnumeric error is spelled #VALVE!. Exact invalid-input tokens are unresolved here; no corrected spelling is presented as observed behavior. Endpoints, omitted-bound combinations and malformed arguments are excluded from the controls. The documented legacy signature is kept distinct from any modern dotted name.

For a beta(2,2) model on [0,1], the CDF is 3*x^2 − 2*x^3. At x = 0.25 this equals 0.15625.

1. Enter 0.15625, 2, 2, 0 and 1 in B1:B5.
2. Use =BETAINV(B1,B2,B3,B4,B5) in B7.
3. The independently known quantile is 0.25.
4. Substitute it into the CDF polynomial to verify the requested probability exactly.

The inverse’s output is an x coordinate on the model’s interval. The input 0.15625 is a probability; they are different quantities even though both happen to lie between zero and one in this example.

These values are exact mathematical roots, not claims that a numerical WPS solver stores those exact binary outputs.

An inverse check should ask how close the cumulative probability at a candidate x is to the requested p. A small error in x can correspond to different probability errors where the density is high or low. For the beta(2,2) control, evaluating the polynomial at 0.25 gives zero probability residual exactly.

This also clarifies interval interpretation: a quantile at p does not assert that exactly p of a small observed dataset lies below it. It belongs to the specified theoretical distribution. Parameter estimation, model suitability and empirical percentiles are separate questions.

WPS states that BETAINV solves the forward cumulative equation and that its accuracy depends on BETADIST. The lesson describes an iterative search and #N/A if it has not converged after 100 iterations. This is historical documentation, not a convergence guarantee or an implementation test in this guide.

The vendor example uses probability 0.8840545, shapes 6 and 9, and bounds 1 and 5, displaying 3.20771369. That is a shifted-interval quantile; original controls deliberately retain explicit [0,1] bounds and elementary exact equations.

Avoid probabilities typed as whole percentages, such as 75 instead of 0.75. No endpoint error, full-range precision or alternate-name availability is inferred. For a discrete probability-table calculation, see PROB; its outputs and inputs have a different contract.

The official WPS lesson is dated 2019-06-14 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.