LAPLACE Function (Gnumeric)

• Introduced: Introduced in Gnumeric 1.1.7 release notes.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Statistics 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.

LAPLACE(x,scale) returns the density EXP(-ABS(x)/scale)/(2*scale) of a Laplace distribution centered at zero. The second argument is a positive scale. The versioned help labels it “mean,” but the implementation and native symmetry tests show that it controls spread, not location. A density is not the probability of a single exact value and may exceed one. Versioned function help.

=LAPLACE(x,scale)

Both arguments are required. To use a center other than zero, subtract that center from x yourself.

Current worksheet implementation.

The native column comes from saved recalculated formulas. The separate reference column evaluates the stated mathematical model, preserving approximation differences. Results are rounded to twelve decimal places, or thirteen significant digits for small nonzero values; printed precision is not a universal accuracy guarantee.

For measurements centered at 10 with scale 2, a measurement of 11 has residual 1. Use =LAPLACE(11-10,2); independent calculation gives about 0.151632664928. Place the measurement in A2, center in B2 and scale in C2, then use =LAPLACE(A2-B2,C2). Keep the measurement and scale in the same units.

For a set of residuals, this formula can supply a density column for a chart or a specified likelihood model. It does not estimate the center or scale from observations. The reference table includes equal positive and negative residuals to demonstrate the centered symmetry.

For a centered Laplace variable with scale b, the mathematical probability of falling within distance d ≥ 0 of the center is 1-EXP(-d/b). At b = 1 and d = 2 this is about 0.864664716763. This interval probability comes from integrating the density; it is not the value of LAPLACE(2,1).

The distribution has mean zero and variance 2*b^2, so a scale of 1 gives variance 2. At x = 0, the peak is 1/(2*b); the native scale-0.1 example gives 5, which is a valid density. The saved symmetry subtraction at x = ±1 returned zero.

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

Zero and negative scales produced #NUM!, including the zero-value/zero-scale case. Very distant values can underflow to zero: =LAPLACE(1000,1) returned zero even though the exact density is positive. A displayed zero does not prove a mathematically impossible observation.

Numeric text was accepted, nonnumeric text produced #VALUE!, and the empty reference acted as x = 0. Too few or too many arguments produced #N/A. If your worksheet stores a mean in the second argument because of the misleading help label, correct the model: subtract the mean from the first argument and put a positive scale in the second.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current random_laplace_pdf calculation
• Tested-version random_laplace_pdf calculation
• Nonfinite worksheet-value handling
• Statistics plugin declaration

The complete callback and inspected calculation helpers are unchanged between these source versions. Both stale and uncached SUM controls recalculated correctly. Native XML retains the function identities; secondary ODF export does not establish execution in another product. GUI entry, other locales and newer-release numerical behavior were not tested.

ABS, EXP, R.DNORM.