R.PGUMBEL Function (Gnumeric)

• Introduced: Introduced in Gnumeric 1.12.25 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.

With z=(x−location)/scale, the lower CDF is EXP(−EXP(−z)). Upper-tail mode gives its complement. Optional log_p selects the natural logarithm of the requested probability. This is the maximum-type Gumbel convention. Versioned function help.

=R.PGUMBEL(x,location,scale[,lower_tail[,log_p]])

x, location and positive scale are required. lower_tail defaults to TRUE and log_p to FALSE. Negative observations and negative locations are valid; a nonpositive scale is not.

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.

At the location itself, the lower probability is EXP(−1), approximately 0.367879441171, rather than 0.5. With location 0 and scale 1, x=1 has lower probability approximately 0.692200627555.

For location 2, scale 1 and cutoff 2.5, the CDF is approximately 0.545239211893. The upper and lower calls at that cutoff add to one in the saved advanced check. Location is therefore not a median parameter.

The lower log-tail is exactly −EXP(−z) mathematically. At x=1 under the standard parameters, it is approximately −0.367879441171. The upper log-tail is different: LN(1−EXP(−EXP(−z))).

For a far-left observation x=−100, the tested ordinary lower probability became zero while its log remained finite. For far-right x=1000, however, the internal EXP(−z) underflow caused the upper log-tail failure in the warning. Requesting a log result does not automatically avoid every intermediate underflow.

The saved advanced-check result for =R.PGUMBEL(2.5,2,1)+R.PGUMBEL(2.5,2,1,FALSE()) was 1.

Zero or negative scale gives #NUM!. The tested extreme ordinary probabilities include rounded zero and one; these are finite-machine outcomes for a distribution whose finite-cutoff probabilities are mathematically between them. The right-tail failure is separately retained rather than described as an invalid mathematical probability input.

Numeric text is parsed, nonnumeric text gives #VALUE!, and empty F5 becomes x=0. Wrong arity gives #N/A. The current 1.12.62 helper is byte-identical to the inspected tested-version helper, but its numerical execution remains unverified.

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

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

EXP, LN, R.PNORM.