R.DCAUCHY 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.DCAUCHY returns Cauchy density or natural log density. The location parameter is its center, median and mode; it is not a finite mean. Scale is a positive width parameter, not a standard deviation. The Cauchy distribution has no finite mean or variance. Versioned function help.

=R.DCAUCHY(x,location,scale[,give_log])

• x: observation.
• location: required center.
• scale: required positive width parameter.
• give_log: optional, FALSE by default. TRUE returns natural log density.

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, density at the center is 1/PI()≈0.318309886184. At x=1 or x=−1 it is half that value. For location 10 and scale 3, the center density is 1/(3π)≈0.106103295395.

A density value is not the probability of a single outcome. To obtain a probability over an interval, use the distribution’s cumulative probabilities at the interval bounds rather than summing density heights without accounting for interval widths.

With z=(x−location)/scale, density is 1/(PI()*scale*(1+z²)). Its log is −LN(PI()*scale*(1+z²)). These formulas explain why shifting the location translates the curve and increasing the scale lowers its height.

The executed check =R.DCAUCHY(2,0,2)*2-R.DCAUCHY(1,0,1) is zero. Both positions have standardized value 1; their densities differ by the inverse scale. At x=5, location 0 and scale 1, the density is 1/(26π)≈0.012242687930. The slowly decreasing tail is a defining feature of this model, not a reason to label its scale as a standard deviation.

The saved advanced-check result for =R.DCAUCHY(2,0,2)*2-R.DCAUCHY(1,0,1) was 0.

Zero or negative scale gives #NUM!. Nonnumeric text gives #VALUE!, while the tested numeric string converts to its number. F5 is a genuinely empty cell and converts to zero. Use positive scale and a deliberate location; neither is optional in this worksheet function.

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 dcauchy 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.

PI, LN, ATAN.