R.QNBINOM Function (Gnumeric)

• Introduced: First release not established; present in the retained 1.12.57 source.
• 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.QNBINOM returns a negative-binomial failure-count threshold. For ordinary positive size and 0<p<1, an interior lower-tail probability selects the smallest nonnegative integer k whose CDF reaches that probability. Integer size has the trials-until-success interpretation; positive noninteger size remains a mathematical shape. Versioned function help.

=R.QNBINOM(probability,size,success_probability[,lower_tail[,log_p]])

• probability: required probability in [0,1], or its natural logarithm; validate it explicitly.
• size: required nonnegative shape; a positive integer describes the target number of successes. Positive noninteger shapes are supported mathematically.
• success_probability: per-trial success chance, with 0<p≤1.
• lower_tail: optional TRUE for a lower-tail probability; FALSE supplies the strict upper-tail probability.
• log_p: optional FALSE. TRUE means the input is a natural logarithm, such as LN(0.1), rather than 0.1.

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 size 3 and p=0.5, the 90% quantile is six failures. P(X≤5)=0.85546875 and P(X≤6)=0.91015625. Adding the three successes gives nine total trials for this threshold. The upper-tail 0.1 and log-upper-tail LN(0.1) examples identify the same count.

At size 1, negative-binomial and geometric count quantiles agree, as the saved difference check shows. Verify the quantile jump using R.PNBINOM(k−1,size,p)<a≤R.PNBINOM(k,size,p) for ordinary interior probabilities. The median in the size-3, p=0.5 example is two because its CDF already equals 0.5 there; a mean of three does not force the median to be three.

The saved advanced-check result for =R.QNBINOM(.9,1,.2)-R.QGEOM(.9,.2) was 0.

For nondegenerate parameters, probability one is unbounded and becomes #NUM!. Degenerate size-zero or p=1 branches instead return zero. The boundary table also preserves zero for probability 1.1 in those branches and for the special size=0,p=0 combination. These out-of-contract observations must not be used as valid quantiles. Negative size and other invalid success probabilities are rejected; nonnumeric text and wrong arity fail separately.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current qnbinom calculation
• Tested-version qnbinom 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.

NEGBINOMDIST, GEOMDIST, R.QBINOM.