R.DRAYLEIGH 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.DRAYLEIGH gives density x/scale²×EXP(−x²/(2scale²)) for positive x, or its natural logarithm. Scale is positive. This is a continuous density on nonnegative observations, not a point probability. Versioned function help.

=R.DRAYLEIGH(x,scale[,give_log])

x and scale are required. Optional give_log defaults to FALSE. x and scale use the same units. The scale is not the Weibull scale: the equivalent Weibull distribution has shape 2 and scale SQRT(2)×RayleighScale.

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 x=1 and scale 1, the density is EXP(−1/2), approximately 0.606530659713. At x=2 it is 2×EXP(−2), approximately 0.270670566473. For scale 2 and x=3, it is approximately 0.243489350519.

A worksheet curve can place nonnegative observations in A2:A20 and use =R.DRAYLEIGH(A2,1). The density is largest at x equal to scale. Probabilities over intervals require integration or the corresponding cumulative model, rather than treating these heights as probability masses.

The executed check compares x=2, scale 1 with Weibull shape 2 and scale SQRT(2), returning zero residual in the selected case. The implementation uses a normal-density relationship instead of directly calling that Weibull expression to avoid introducing an inexact SQRT(2) scale.

The log-density formula is LN(x)−2LN(scale)−x²/(2scale²). At x=1000 and scale 1, the ordinary native density underflows to zero, while the log value remains approximately −499993.092244721. A zero ordinary result at that finite x is numerical underflow, not a zero mathematical density.

The saved advanced-check result for =R.DRAYLEIGH(2,1)-R.DWEIBULL(2,2,SQRT(2)) was 0.

Zero or negative x returns density zero. Asking for its log reaches negative infinity and displays #NUM!. Nonpositive scale also gives #NUM!, for a different reason.

Numeric text is parsed, nonnumeric text gives #VALUE!, and empty F5 behaves as zero. Wrong arity gives #N/A. The direct and log-density cases establish only the retained 1.12.57 examples; the complete helper is unchanged in inspected 1.12.62 source, but that newer build was not executed.

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

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

WEIBULL, R.DNORM, LN.