R.DNBINOM Function (Gnumeric)

• Introduced: First release not established; named in Gnumeric 1.12.10 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.DNBINOM returns a negative-binomial mass. For positive integer size r, it is the probability of x failures before the rth success in independent trials with success chance p. Its generalized mass is Γ(x+r)/(Γ(r)Γ(x+1))×p^r×(1−p)^x; positive noninteger r is a supported shape. Versioned function help.

=R.DNBINOM(failures,size,success_probability[,give_log])

• failures: required nonnegative integer observation; it excludes the successes.
• 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.
• give_log: optional FALSE; TRUE returns a natural log mass.

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 success chance 0.5, exactly two failures before the third success has mass COMBIN(4,2)×0.5^3×0.5^2=0.1875. The terminating trial is a success, so the total trial count in that event is five. Replacing failures by total attempts would change the event.

Size 1 reduces to the geometric distribution. The stored subtraction check compares R.DNBINOM(3,1,0.2) with R.DGEOM(3,0.2); its tiny residual reflects floating-point evaluation rather than a mathematical disagreement. For size 3 and p=0.5, expected failures are r(1−p)/p=3 and variance is r(1−p)/p^2=6. The size=2.5 reference demonstrates a mathematical shape, not “two and a half observed successes.”

The saved advanced-check result for =R.DNBINOM(3,1,.2)-R.DGEOM(3,.2) was -1.387778780781E-17.

Negative sizes and p outside 0<p≤1 are rejected. Size zero is handled as a point mass at zero in the tested ordinary cases; positive failures have mass zero. Fractional failure observations such as 2.9 return zero with a calculation warning rather than being floored. Logarithms of zero masses become #NUM!. Small near-integer differences use the explicit tolerance shown in the source.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current dnbinom calculation
• Tested-version dnbinom calculation
• Nonfinite worksheet-value handling
• Statistical Functions From R plugin declaration
• Near-integer tolerance
• Noninteger mass check

The deliberate fractional count/trial probes also emitted noninteger-input calculation warnings. The saved logs retain them.

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.DBINOM.