R.QRAYLEIGH 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.

R.QRAYLEIGH returns the cutoff with a specified Rayleigh tail probability. For a lower probability p between zero and one, the mathematical quantile is scale×SQRT(−2×LN(1−p)). Upper-tail mode takes the survival probability instead. Versioned function help.

=R.QRAYLEIGH(probability,scale[,lower_tail[,log_p]])

Probability and positive scale are required. lower_tail defaults to TRUE and log_p to FALSE. In ordinary mode use a probability from zero through one; in log mode use its nonpositive natural logarithm. Scale determines observation units.

Brackets mark optional arguments; do not type them. Current worksheet implementation.

These self-contained formulas were recalculated natively. The separate reference column evaluates the stated mathematical distribution; discrepancies are preserved and explained rather than treated as successful mathematical results. Source branches and typed native outputs 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 scale 1, the median is approximately 1.177410022515, and the 90th percentile is 2.145966026289. An upper probability of 0.1 gives the same 90th-percentile cutoff. Entering LN(0.1) requires both lower_tail=FALSE and log_p=TRUE.

If observations and scale are measured in the same units, the result is also in those units. Doubling scale doubles every interior quantile; the scale-2 median is approximately 2.354820045031.

The saved CDF round trip below recovers 0.9 from the computed 90th-percentile cutoff. The equivalent Weibull model has shape 2 and scale SQRT(2) times the Rayleigh scale, explaining the helper’s implementation.

For a central interval, use two lower-tail probabilities, such as 0.1 and 0.9. Do not confuse those inputs with a lower-tail 0.9 and an upper-tail 0.1, which identify the same cutoff. The mathematical median-to-scale ratio is SQRT(2×LN(2)), independent of scale.

The saved advanced-check result for =R.PRAYLEIGH(R.QRAYLEIGH(.9,1),1) was 0.9.

Lower probability zero gives zero. Lower probability one reaches an infinite endpoint and produces #NUM!. Upper endpoints reverse those outcomes. Log probability zero represents probability one, not zero; a positive log probability is invalid.

Zero or negative scale gives #NUM!, including a zero-probability input. Nonnumeric text gives #VALUE!, while empty F5 becomes ordinary probability zero. Wrong argument counts give #N/A. Infinite distribution endpoints are not finite thresholds that can be entered into a downstream comparison as ordinary numbers.

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

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

The relevant complete worksheet callback and inspected calculation helpers are unchanged between the source versions; later numerical execution is not established. 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.

R.DRAYLEIGH, R.QWEIBULL, LN.