R.QCAUCHY 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.QCAUCHY inverts Cauchy probabilities. The default is a lower-tail quantile. With lower_tail=FALSE it finds the cutoff for an upper-tail probability. log_p=TRUE changes the first argument to a natural log probability. Versioned function help.

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

• probability: p or LN(p), according to log_p.
• location and scale: required; use positive scale for an ordinary Cauchy distribution.
• lower_tail: optional, TRUE by default.
• log_p: optional, FALSE by default.

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

These self-contained formulas were recalculated natively and checked against independent mathematics. Results are rounded to twelve decimal places, or thirteen significant digits for small nonzero values. This is presentation precision, not a universal accuracy guarantee.

For location 0 and scale 1, the lower quartile, median and upper quartile are −1,0,1. Thus =R.QCAUCHY(0.75,0,1) and =R.QCAUCHY(0.25,0,1,FALSE()) both return 1. The corresponding log-upper input uses LN(0.25) with the final flag TRUE.

For location 10 and scale 2, the median is 10 and the upper quartile is 12. The interquartile range is twice the scale, so it is 4 in this example. This is a width summary without assuming a finite standard deviation.

For lower-tail p, the mathematical quantile is location+scale*TAN(PI()*(p−0.5)). An upper-tail request reverses the sign of the standardized term. The native 90th percentile of the standard Cauchy is approximately 3.077683537175.

The executed CDF/quantile round trip at p=0.9 returns 0.9. Near endpoints, direct tangent expressions can lose accuracy, while the implementation uses complementary-tail transformations and cotangent. A round trip is a consistency check for the stated case, not universal extreme-tail certification.

The saved advanced-check result for =R.PCAUCHY(R.QCAUCHY(.9,0,1),0,1) was 0.9.

With positive scale, p=0 or p=1 requires an infinite mathematical endpoint and yields #NUM!. Values outside [0,1], positive log probabilities and negative scales also error. The tested zero-scale interior case returns location, but that does not establish an ordinary positive-scale Cauchy distribution. Supply all required parameters explicitly.

F5 is genuinely empty, rather than a cell containing an empty string. #NUM! can represent an unrepresentable infinite mathematical endpoint as well as an invalid numeric domain; the distinctions above matter.

• Current worksheet callback
• Tested-version worksheet callback
• Current qcauchy calculation
• Nonfinite worksheet-value handling
• Statistical Functions From R plugin declaration

The relevant worksheet callback is unchanged between the inspected versions. That does not establish later-version numerical execution. Both stale and uncached SUM controls recalculated correctly. Native XML identities were checked; secondary ODF exports retain these functions with the ORG.GNUMERIC namespace. GUI entry, other locales and other spreadsheet products were not tested.

TAN, ATAN, PI.