R.QBINOM Function (Gnumeric)

• Introduced: First release not established; named in Gnumeric 1.12.1 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.

For an interior lower probability p, R.QBINOM returns the smallest integer count whose cumulative probability reaches p. A discrete inverse usually cannot make the cumulative value equal p exactly. Endpoint and degenerate cases also follow explicit source conventions. Versioned function help.

=R.QBINOM(probability,trials,success_probability[,lower_tail[,log_p]])

• probability: lower target probability by default, or upper probability when lower_tail is FALSE.
• trials: nonnegative integer; this helper uses a stricter integrality check than R.DBINOM or R.PBINOM.
• success_probability: per-trial probability in [0,1].
• lower_tail: optional TRUE for the lower cumulative probability; FALSE requests the upper tail.
• log_p: optional FALSE. TRUE uses natural-log probabilities, not base-10 logarithms.

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; source guards explain the boundary cases. Results are rounded to twelve decimal places, or thirteen significant digits for small nonzero values. This is presentation precision, not a universal accuracy guarantee.

With five trials and success probability 0.5, target 0.75 returns 3. The cumulative probability at 2 is 0.5, while at 3 it is 0.8125. Thus 3 is the first integer threshold reaching the target, even though 0.8125 is not 0.75.

With ten trials and success probability 0.4, target 0.3 also returns 3: the independent cumulative probabilities at 2 and 3 are 0.1672897536 and 0.3822806016. Do not interpolate a fractional count between those jumps.

Upper-tail input 0.25 selects the same count as lower-tail input 0.75. Its meaning is a complementary target, not a requirement that the strict upper cumulative probability equal 0.25 exactly. The source slightly adjusts a search probability for floating-point continuity near cumulative jumps.

Log mode can use LN(0.25) with lower_tail FALSE and log_p TRUE. In the saved advanced check, evaluating R.PBINOM at the returned 0.75 quantile produces 0.8125, deliberately demonstrating the discrete jump rather than an exact continuous inverse.

The saved advanced-check result for =R.PBINOM(R.QBINOM(.75,5,.5),5,.5) was 0.8125.

Endpoint conventions precede degenerate-distribution shortcuts. In default lower-tail mode, p=0 returns 0 and p=1 returns n, even when the success probability is respectively 1 or 0. Thus the tested R.QBINOM(1,5,0) returns 5, although all distribution mass is at zero. Validate the intended endpoint convention before using a threshold for a degenerate model.

Trials 5.000000000000001 give #NUM! here, unlike the tolerant mass/CDF helpers. Negative or fractional trials, invalid success probabilities and invalid target probabilities also error. Empty p becomes zero; log input zero means ordinary probability one. Nonnumeric text is #VALUE! and incorrect arity is #N/A.

F5 is genuinely empty, rather than a cell containing an empty string.

• Current worksheet callback
• Tested-version worksheet callback
• Current qbinom calculation
• Tested-version qbinom calculation
• Nonfinite worksheet-value handling
• Statistical Functions From R plugin declaration
• Quantile boundary convention

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 preserves the R.* identities. The secondary ODF export keeps these calls in the ORG.GNUMERIC namespace; it does not establish execution in another product. GUI entry, other locales and other spreadsheet products were not tested.

CRITBINOM, BINOMDIST, BINOM.DIST.RANGE.