EXPPOWDIST 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.

EXPPOWDIST(x,scale,shape) implements the symmetric exponential-power density EXP(-(ABS(x)/scale)^shape)/(2*scale*GAMMA(1+1/shape)) for positive scale and shape. It is centered at zero and extends over the whole real line. The help’s second “scale” label actually refers to shape, and its lifetime/U-shaped-hazard description does not describe this symmetric implemented density. Use the formula and parameter meaning given here. Versioned function help.

=EXPPOWDIST(x,scale,shape)

All three arguments are required. The function has no cumulative flag or explicit location argument.

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 a symmetric model centered at 10, with scale 2 and shape 2, use =EXPPOWDIST(11-10,2,2). Independent calculation gives about 0.219695644734. In a worksheet with measurement A2, center B2, scale C2 and shape D2, use =EXPPOWDIST(A2-B2,C2,D2) after validating positive scale and shape.

The direct native table compares both signs of x and the shape-1, shape-2 and shape-0.5 cases. This function evaluates a chosen density; it does not estimate the parameters or establish that a lifetime model is appropriate.

With shape = 1, the formula becomes the centered Laplace density with the same scale. The saved subtraction from LAPLACE(1,1) returned zero. With shape = 2, it becomes a normal density with standard deviation scale/SQRT(2), not scale itself. Thus scale 2 and shape 2 have variance 2.

More generally the mathematical variance is scale^2*GAMMA(3/shape)/GAMMA(1/shape). For valid positive parameters, the total density integrates to one. The peak at x = 0 can exceed one for sufficiently small scales; that is compatible with density semantics and should not be confused with the invalid negative-density behavior below.

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

The tested nonpositive shapes produced #NUM!. Zero scale also produced #NUM! in the two saved cases, but through nonfinite arithmetic rather than a positive-scale guard. With scale −1 and shape 2, the native values were negative: about −0.207553748710 at x = 1 and −0.564189583548 at x = 0. Reject negative scale even if the function returns a finite number.

A distant value underflowed to zero. Numeric text was accepted, nonnumeric text produced #VALUE!, and the empty x reference acted as zero. Wrong argument counts produced #N/A. The inspected newer source retains the same scale-check omission; this guide does not claim newer execution.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current random_exppow_pdf calculation
• Tested-version random_exppow_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.

R.DNORM, GAMMA, ABS.