R.PST Function (Gnumeric)

• Introduced: Implementation documented in Gnumeric 1.12.2 release notes. Earlier registration history was not established here.
• 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.PST is the cumulative function for the standardized skew-t distribution, with lower, upper and log-probability modes. Shape zero delegates to Student t. Nonzero shape uses a recurrence for integer degrees of freedom up to 100, then a skew-normal approximation above that threshold. Versioned function help.

=R.PST(x,degrees_freedom,shape[,lower_tail[,log_p]])

x, degrees_freedom and shape are required. Degrees of freedom must be positive. lower_tail defaults to TRUE and log_p to FALSE. For nonzero shape, fractional df at or below 100 is unsupported by the inspected CDF helper; fractional df above 100 enters the approximation branch.

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.

At x=1, df=5 and shape=2, the ordinary lower probability is approximately 0.643516606084 and the upper is 0.356483393916. These ordinary calls agree with independent integration of the skew-t density.

The correct natural logs are approximately −0.440807446399 and −1.031467621093. The 1.12.57 calls with log_p=TRUE instead repeat the positive ordinary probabilities. For this moderate, nonzero ordinary probability, taking LN of the checked ordinary result gives the mathematical log; this is not a general protection against probability underflow.

The 1.12.57 helper computes a logarithm in its fallback branch but omits return, so execution continues into the ordinary recurrence. The inspected 1.12.62 line returns that logarithm. The advanced difference below is therefore approximately 1.084324052483 in the old engine rather than zero.

At df=101, shape=2 and x=1, the engine returns the skew-normal probability 0.684408372082. Independent integration of the finite-df skew-t density gives approximately 0.682206548866. This is an explicit approximation, separate from the log defect. The approximation also inherits the large-shape limitations of R.PSNORM.

The saved advanced-check result for =R.PST(1,5,2,TRUE(),TRUE())-LN(R.PST(1,5,2)) was 1.084324052483.

The tested nonzero-shape df=2.5 call returns #NUM!, while shape zero at the same df works through Student t. A noninteger df=100.5 enters the skew-normal approximation rather than the unsupported recurrence. These branches must not be summarized as “all positive df behave alike.”

Zero or negative df gives #NUM!. Nonnumeric text gives #VALUE!, empty F5 becomes zero, and wrong arity gives #N/A. At x=0, the mathematical lower probability is 1/2−ATAN(shape)/PI() for every positive df, but the large-negative-shape approximation can still violate it. Treat the source fix as documentary evidence, not a later native test.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current pst calculation
• Tested-version pst calculation
• Current psnorm calculation
• Tested-version psnorm calculation
• 1.12.62 log-case fix release note
• Nonfinite worksheet-value handling
• Statistical Functions From R plugin declaration

The worksheet callbacks are unchanged. The PST helper differs by the missing return fixed in 1.12.62; no newer inverse or CDF execution is inferred. 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.PT, R.DT, LN.