R.DST Function (Gnumeric)

• Introduced: Introduced in Gnumeric 1.9.15 release notes.
• 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.DST gives the skew-t density, or its natural logarithm. With degrees of freedom ν>0 and shape α, its density at x is 2tν(x)Tν+1(αx×SQRT((ν+1)/(ν+x²))). Here t is Student-t density and T its cumulative distribution. Versioned function help.

=R.DST(x,degrees_freedom,shape[,give_log])

x, degrees_freedom and shape are required. Degrees of freedom must be positive and may be fractional for this density helper. Optional give_log defaults to FALSE. This interface has no location or scale arguments; it uses the standardized skew-t model.

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.

For ν=5 and shape 2, density at x=1 is approximately 0.419055401315, while density at x=−1 is 0.020304193387. Reversing shape to −2 mirrors the density. Shape zero reduces to Student t; the executed comparison below gives zero difference from R.DT in the selected case.

A density column can evaluate =R.DST(A2,5,2) for observations in A2:A20. Those heights are not probabilities of individual observations and should not be summed as discrete probability masses.

At x=0, the second CDF factor is one half, so the density equals the symmetric Student-t density at zero for any finite shape. With ν=5 the value is approximately 0.379606689822.

The fractional-df example ν=2.5 works in this density function, returning approximately 0.376263815524 at x=1 and shape 2. R.PST has a narrower nonzero-shape fractional-df branch, so successful density evaluation does not establish cumulative or inverse support for the same parameters. For ν=101, this density still evaluates the skew-t expression; R.PST instead uses a skew-normal approximation above 100.

The saved advanced-check result for =R.DST(1,5,0)-R.DT(1,5) was 0.

Zero or negative degrees of freedom gives #NUM!. Negative observations and negative shape are valid. Numeric text is parsed, nonnumeric text gives #VALUE!, and empty F5 behaves as x=0. Incorrect argument counts give #N/A.

The optional log form is the logarithm of a density and can be negative without indicating an error. It is separate from R.PST’s log-probability flag and does not share that helper’s tested missing-return bug. The inspected density helper is unchanged between the two source versions, while only 1.12.57 was executed.

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

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

The relevant complete worksheet callback and inspected calculation helpers are unchanged between the source versions; later numerical execution is not established. 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.DT, R.PT, LN.