R.DF Function (Gnumeric)

• Introduced: First release not established; present in the retained 1.12.57 source.
• 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.DF evaluates the continuous F density. Numerator and denominator degrees of freedom have different roles. A density value is not the probability of observing exactly that value, and it is not an F-test p-value. Versioned function help.

=R.DF(x,numerator_df,denominator_df[,give_log])

• x: observation on the nonnegative F scale; negative x has zero density.
• numerator_df, denominator_df: positive real degrees of freedom; fractions are retained.
• give_log: optional FALSE; TRUE returns the natural logarithm of the density or probability 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 both degrees equal to 2, the density simplifies to 1/(1+x)^2. Thus x=1 gives 0.25, x=2 gives 0.111111111111, and x=0.5 gives 0.444444444444. These values describe the height of a continuous density.

The corresponding probability between 0.5 and 2 is an integral, independently equal to 1/3 for this model. Subtracting the two density heights would not calculate that probability.

For positive x, the density is proportional to (d1/d2)^(d1/2)*x^(d1/2-1)/(1+d1*x/d2)^((d1+d2)/2), normalized by B(d1/2,d2/2). The independent checks use that beta-function expression.

Reciprocating an F variable swaps the degrees and introduces a Jacobian: f(x;d1,d2)=f(1/x;d2,d1)/x². The saved advanced check tests this at x=2, d1=5 and d2=10. Log mode is useful when adding density contributions without first multiplying very small values.

The saved advanced-check result for =R.DF(2,5,10)-R.DF(.5,10,5)/4 was 0.

The zero boundary depends on the numerator degree: d1<2 has infinite density and yields #NUM!; d1=2 returns 1, with log density 0; d1>2 returns zero. This is independent of the denominator degree when it is positive.

Negative x returns zero, whose logarithm is an unrepresentable negative infinity and therefore #NUM!. Nonpositive degrees also give #NUM!. Empty F5 becomes zero, so the example with d1=2 returns 1. Nonnumeric text is #VALUE!, and incorrect arity is #N/A.

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

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

FDIST, FINV, R.DGAMMA.