R.PF 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.PF returns the lower cumulative F probability by default. FALSE selects the upper tail. The first degree belongs to the numerator of the F ratio, and the second to the denominator. Versioned function help.

=R.PF(x,numerator_df,denominator_df[,lower_tail[,log_p]])

• x: real cutoff; at or below zero the lower probability is zero.
• numerator_df, denominator_df: required positive real parameters.
• lower_tail: optional TRUE for the lower cumulative probability; FALSE requests the upper tail.
• log_p: optional FALSE. TRUE uses natural-log probabilities, not base-10 logarithms.

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 degrees 2 and 2, the CDF is x/(1+x) for x≥0. At x=2, R.PF gives 2/3; the upper-tail mode gives 1/3. The result is a probability, unlike the density returned by R.DF.

For an F statistic constructed as a specified sample-variance ratio, pass the matching sample-count-minus-one degrees in that same order. An upper-tail probability can be relevant to a pre-specified directional variance comparison, but this function does not choose or perform the entire test for you.

The beta representation uses z=d1x/(d2+d1x) and shapes d1/2,d2/2. It explains why the argument is not a raw beta probability. Direct upper-tail evaluation avoids subtracting a near-one result when the desired probability is small.

For positive x, reciprocity gives F(x;d1,d2)+F(1/x;d2,d1)=1. The saved check uses x=2, d1=5 and d2=10. For the simple degrees-2 model, the interval 0.5<X≤2 has probability 2/3−1/3=1/3.

The saved advanced-check result for =R.PF(2,5,10)+R.PF(.5,10,5) was 1.

Zero and negative cutoffs return lower probability zero; the corresponding upper probability is one. Their log probabilities are respectively negative infinity, displayed as #NUM!, and zero. Invalid nonpositive degrees are rejected rather than treated as a zero-cutoff shortcut.

Fractional positive degrees are retained. Empty F5 becomes zero, nonnumeric text produces #VALUE!, and missing or extra arguments produce #N/A. Log mode reports LN(probability), so its negative output should not be formatted as an ordinary probability percentage.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current pf calculation
• Tested-version pf 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.PGAMMA.