R.PBETA Function (Gnumeric)

• Introduced: First release not established; named in Gnumeric 1.5.2 release notes.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Statistical Functions From R plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. Tables and the named advanced check use 1.12.57 ssconvert. Current 1.12.62 source was inspected; that release was not executed.

R.PBETA returns the beta cumulative probability P(X≤x), or the upper-tail probability P(X>x) when lower_tail is FALSE. For a continuous model, both shapes must be positive. The help’s second “scale” label is misleading: beta is a second shape, and the support remains [0,1]. Versioned function help.

=R.PBETA(x,alpha,beta[,lower_tail[,log_p]])

• x: cutoff on the unit interval; valid shapes give cumulative 0 below support and 1 above it.
• alpha, beta: required positive shapes.
• lower_tail: optional, defaults to TRUE; FALSE requests the upper tail.
• log_p: optional, defaults to FALSE; TRUE returns the natural logarithm of the selected probability.

Brackets mark optional arguments; do not type them. Current worksheet implementation.

These self-contained formulas were recalculated natively. Ordinary-domain results were checked against independent mathematics; invalid-model observations are identified separately below. Results are rounded to twelve decimal places, or thirteen significant digits for small nonzero values. This is presentation precision, not a universal accuracy guarantee.

For alpha=1, beta=4 and x=0.4, =R.PBETA(0.4,1,4) gives 0.8704. The upper tail is 0.1296, obtained with FALSE as the fourth argument. These are complementary events under the same model.

With shapes 2,3, the probabilities at x=0.25 and x=0.75 are 0.26171875 and 0.94921875. Their difference, 0.6875, is the probability between those cutoffs. No density approximation is needed.

The beta CDF is the regularized integral of t^(alpha-1)*(1-t)^(beta-1) from 0 to x. For Beta(1,4), the upper tail simplifies to (1-x)^4; at x=0.4 it is 0.6^4=0.1296. Its natural logarithm is approximately −2.043302495064.

Request a small upper tail directly rather than subtracting a probability near 1. The advanced check adds the two directly calculated tails for the same cutoff and parameters.

The saved advanced-check result for =R.PBETA(.4,1,4)+R.PBETA(.4,1,4,FALSE()) was 1.

The nonpositive-shape rows are observed invalid-input behavior, not mathematical beta probabilities. In particular, the tested inputs (x,alpha,beta)=(0.5,0,2) and (0.5,−1,2) returned approximately 0.305555555556 and 0.5859375. The inspected helper lacks a positive-shape guard. Check both shapes explicitly before using any result.

For valid shapes, a zero selected probability has logarithm −∞ and appears as #NUM!; the ordinary probability remains 0. A genuinely empty cutoff cell is converted to zero. These endpoint and conversion effects are different from the shape-validation defect.

F5 is genuinely empty, rather than a cell containing an empty string. #NUM! can represent an unrepresentable infinite mathematical endpoint as well as an invalid numeric domain; the distinctions above matter.

• Current worksheet callback
• Tested-version worksheet callback
• Current pbeta calculation
• Tested-version pbeta calculation
• Nonfinite worksheet-value handling
• Statistical Functions From R plugin declaration

The relevant complete worksheet callback and main calculation helper are unchanged between the inspected versions. That does not establish later-version numerical execution. Both stale and uncached SUM controls recalculated correctly. Native XML identities were checked; secondary ODF exports retain these functions with the ORG.GNUMERIC namespace. GUI entry, other locales and other spreadsheet products were not tested.

BETADIST, BETA, LN.