R.DT 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.DT returns the density of the standard Student t distribution at x. It is centered at zero, and degrees_freedom controls the tail shape. It does not return a one- or two-tailed p-value and does not estimate a location or scale from data. Versioned function help.

=R.DT(x,degrees_freedom[,give_log])

• x: real observation on the standard t scale.
• degrees_freedom: required positive real value; fractional values are allowed.
• give_log: optional FALSE; TRUE requests natural log-density. A nonzero numeric flag, such as 2 in the boundary test, is treated as true.

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; invalid-model observations are identified separately below. 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 one degree of freedom, the density is 1/(PI()*(1+x^2)), the standard Cauchy density. At zero it is approximately 0.318309886184; at either x=1 or x=−1 it is approximately 0.159154943092.

For x=2 and 5 degrees of freedom, density is approximately 0.065090310326. A density height does not itself tell you the probability beyond x=2; that requires integration or the matching cumulative function.

For ν>0 the density is GAMMA((ν+1)/2)/(SQRT(ν*PI())*GAMMA(ν/2))*(1+x^2/ν)^(-(ν+1)/2). The function’s direct log option corresponds to the logarithm of this expression.

The saved advanced check compares x=1 and x=−1 at the same degree of freedom. Symmetry holds about zero. The large-x Cauchy example retains a small positive density near 3.183098861835×10^−13 and a log-density near −28.775751001779; it is not rounded to zero in the table.

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

Degrees of freedom must be positive; zero and negative values produced #NUM!. The 2.5-degree reference confirms that fractional degrees are not silently rounded. Numeric text was converted, whereas nonnumeric x or flag text produced #VALUE!.

If your data have location μ and positive scale s, a separately specified location-scale t model has density R.DT((x-μ)/s,ν)/s. The division by s is essential for a density, although the tested function itself has no location or scale arguments. The standard t distribution has heavy tails; do not use a normal density as an interchangeable formula.

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 dt calculation
• Tested-version dt 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 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.

TDIST, R.DNORM, R.DCAUCHY.