PARETO 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.

PARETO(x,shape,minimum) evaluates the Type I Pareto density. For x at least the positive minimum, it returns shape/minimum*(x/minimum)^(-shape-1); below the minimum it returns zero. The help calls the shape an exponent and the minimum a scale parameter. Here “minimum” makes the lower support boundary explicit. Versioned function help.

=PARETO(x,shape,minimum)

All three arguments are required, in this order.

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 positive-size model with minimum 2 and shape 3, =PARETO(4,3,2) gives 0.09375. At the minimum, =PARETO(2,3,2) gives 1.5. That density can exceed one; it is not a probability. A value of 1 is below the modeled support and has density zero.

Put x in A2, shape in B2 and minimum in C2, then use =PARETO(A2,B2,C2). Estimate or choose those model parameters separately; the function neither fits a tail model nor checks that the data are appropriate for one.

For x ≥ minimum, the mathematical survival probability is (minimum/x)^shape. With x = 4, shape 3 and minimum 2 it is 0.125; the probability between 2 and 4 is 0.875. These are integrated probabilities, unlike the density 0.09375 at x = 4. The saved identity =PARETO(4,3,2)*4/3 returned 0.125.

A finite mean exists only for shape > 1, and a finite variance only for shape > 2. Their formulas are shape*minimum/(shape-1) and shape*minimum^2/((shape-1)^2*(shape-2)). At shape 3 and minimum 2, both the mean and variance are 3. The density itself remains meaningful for smaller positive shapes even when those moments do not exist.

The saved advanced-check result for =PARETO(4,3,2)*4/3 was 0.125.

Nonpositive shape or minimum produced #NUM!. With valid parameters, negative x and zero x returned zero because they lie below the support. The native table also includes shape 0.5, showing that the function does not require a finite mean.

Numeric text was converted, nonnumeric text produced #VALUE!, and an empty x reference acted as zero. Missing or additional arguments produced #N/A. Do not confuse this three-argument density with a Pareto chart, percentile rule or cumulative distribution.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current random_pareto_pdf calculation
• Tested-version random_pareto_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.

POWER, EXP, R.PWEIBULL.