LOGISTIC 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.

LOGISTIC(x,scale) returns the density of a zero-centered logistic distribution. With u=EXP(-ABS(x)/scale), the implemented density is u/(scale*(1+u)^2). This is a symmetric bell-shaped density. It is not the sigmoid CDF often called a logistic function, and it does not fit logistic regression. Versioned function help.

=LOGISTIC(x,scale)

Both inputs are required. There is no location argument or cumulative flag.

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 distribution centered at 10 with scale 2, evaluate a measurement of 11 with =LOGISTIC(11-10,2). The independent density is about 0.117501856101. With measurement A2, center B2 and scale C2, use =LOGISTIC(A2-B2,C2). These cell formulas express the stated model; the direct native table independently checks the basic density and its scale behavior.

For comparison, at x = 1 and scale = 1 the density is about 0.196611933241, whereas the mathematical lower-tail CDF =1/(1+EXP(-1)) is about 0.731058578630. Choose the density or probability according to the quantity you actually need.

The maximum density occurs at zero and equals 1/(4*scale). Doubling scale from 1 to 2 halves that peak, as the table shows. A scale of 0.1 gives peak density 2.5; density values above one are valid because probabilities are areas.

For scale 1, the mathematical probability between −2 and 2 is TANH(1), about 0.761594155956. The variance is PI()^2/3, about 3.289868133696. These are independent model calculations, not extra native tests. The saved direct subtraction at x = ±1 returned zero, confirming the selected symmetry case.

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

The second argument must be positive. Zero and negative scales produced #NUM!; the helper’s use of an absolute value does not override the worksheet wrapper’s positive-scale guard. At x = 1000 and scale = 1 the native density underflowed to zero.

Numeric text was converted, nonnumeric text produced #VALUE!, and an empty x cell produced the peak for x = 0. Wrong argument counts produced #N/A. For shifted models, subtract the center before calling LOGISTIC; putting a mean in the scale position changes spread instead of shifting the curve.

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

• Current worksheet callback
• Tested-version worksheet callback
• Current random_logistic_pdf calculation
• Tested-version random_logistic_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.

EXP, TANH, R.DNORM.