NEGBINOM.DIST in Collabora Office: Count Failures Before a Target Number of Successes

=NEGBINOM.DIST(X; R; SP; Cumulative)

X is the count of unsuccessful attempts before the target success is achieved. R is the required success count, and SP is the success probability on an attempt. Cumulative=0 selects the exact-count probability; Cumulative=1 selects the cumulative probability through X. Supply all four arguments.

For the ordinary model use integer X>=0, integer R>=1 and 0<SP<1. Attempts are independent with the same success probability. The stopping rule is “continue until R successes,” rather than “take a fixed number of attempts.”

The documentation calls the zero-flag result a density; because this is a discrete count model, it is a probability mass. It can be interpreted as the probability of an exact integer failure count. Total attempts equal X+R, so failures and total attempts must not share the same column label.

Put 0, 1, 2, 3, 4 in A2:A6. Put target successes 2 in F2 and success probability 0.5 in F3. In B2 enter =NEGBINOM.DIST(A2;$F$2;$F$3;0) and fill down.

Independent exact-count targets are 0.25, 0.25, 0.1875, 0.125 and 0.078125. Put =A2+$F$2 in C2 and fill down to show total attempts 2, 3, 4, 5 and 6.

For exactly two failures before the second success, the last attempt must be a success. Among the first three attempts, exactly one is successful. There are three arrangements, each with probability (0.5)^4, yielding 3/16=0.1875. This verifies the stopping-rule interpretation directly.

Use =NEGBINOM.DIST(A2;$F$2;$F$3;1) in D2 and fill down. Independent cumulative targets are 0.25, 0.5, 0.6875, 0.8125 and 0.890625.

Achieving two successes within four total attempts means at most two failures before the second success. The formula is =NEGBINOM.DIST(4-2;2;0.5;1), independently 0.6875. Supplying X=4 would instead allow six total attempts.

For more than two failures, use =1-NEGBINOM.DIST(2;2;0.5;1), independently 0.3125. “At least two failures” instead subtracts the cumulative probability through one and targets 0.5. The exact count two has positive probability, so these events differ.

The event “the second success occurs by attempt four” is equivalent to “at least two successes occur in four attempts.” Under the same independent probability-one-half model, the latter binomial event has probability 0.6875.

Direct enumeration gives one outcome with no successes and four outcomes with exactly one among sixteen equally likely four-attempt sequences. Removing those five leaves eleven, or 11/16. This checks the cumulative negative-binomial result without confusing the two functions’ count arguments.

With R=1, the model is a geometric waiting count of failures before the first success. The official examples =NEGBINOM.DIST(1;1;0.5;0) and =NEGBINOM.DIST(1;1;0.5;1) have independent targets 0.25 and 0.75.

The mean failure count for the ordinary model is R*(1-SP)/SP. With R=2 and SP=0.5, that is 2 failures, while the mean total attempts R/SP is 4. A mean is not a guaranteed stopping time, and the possible failure count is unbounded.

Validate integer counts and an interior success probability. The dedicated help does not certify fractional-count coercion, degenerate probability boundaries or native error codes; these remain unverified.

If results appear shifted, check whether X counts failures or all attempts. If the process has changing success probabilities, dependence or sampling without replacement, the fixed-probability independent-attempt model may be unsuitable even when the formula returns a number.

The exact function is documented in Collabora Office 26.04 desktop help. Its source snapshot was retrieved on 2026-10-13 and hash-verified for this guide on October 15, 2026. Desktop documentation is not proof of Online or mobile support.

First introduced release and last functioning version are unknown. The available dedicated source does not establish those releases. No native Collabora or WPS run occurred. Numerical values are independent mathematical expectations, not certification of application-specific errors, numerical tolerances or all edge cases. Formulas use English names and semicolon separators.

The help identifies the namespace COM.MICROSOFT.NEGBINOM.DIST and says this function is outside the cited OpenFormula 1.3 standard. This format disclosure does not prove identical behavior in another product. Keep exact dotted names when checking imported workbooks.

• Collabora Office 26.04: NEGBINOM.DIST.
• Editorial testing standards.