RANDLOGISTIC Function (Gnumeric)

• Introduction: Gnumeric 1.1.6 NEWS explicitly lists this new function. This release-history evidence is separate from a native test of that old version.
• Source support: Registered in the Gnumeric 1.12.62 random plugin. No retirement is established; the last functioning native application version is unverified.
• Evidence dates: Official Gnumeric source retained October 13–14, 2026 was reviewed October 15. Mathematical controls were independently recalculated October 15. No native application, compiled Gnumeric helper or random generator was executed.

The single required argument a is nonnegative. A negative scale produces #NUM!. The helper obtains a unit driver U, rejects 0 or 1, and evaluates a*LN(U/(1-U)). This is an increasing inverse-CDF mapping for the zero-location logistic distribution.

At positive scale the ideal mean and median are0, and variance is a²*PI()²/3. Scale is therefore different from standard deviation. The function has no explicit location or seed argument.

Create LogisticControls. Put scale 2 in B2 and location 10 in B3. In D2 enter =RANDLOGISTIC($B$2). In D3 enter =$B$3+D2 to shift that same variate. Both results vary, while their difference is10 apart from ordinary addition rounding.

In F2 enter =$B$2*PI()/SQRT(3). The independent result is approximately 3.62759872847, the ideal standard deviation. In F3 enter =$B$2^2*PI()^2/3, approximately 13.1594725348, for the ideal variance. These are population parameters rather than exact summaries of a finite random sample.

Put 0.1, 0.25, 0.5, 0.75 and 0.9 in A7:A11. In B7 enter =$B$2*LN(A7/(1-A7)) and fill down. These supplied drivers yield:

The middle driver0.5 gives 0. Opposite drivers U and1-U produce opposite mathematical values, illustrating the distribution’s symmetry. Do not include0 or 1 in this literal worksheet: the source retries those endpoints, while a single LN expression cannot perform that retry.

For scale 2, the ideal25th and75th percentiles are approximately -2.19722457734 and 2.19722457734. Adding location 10 moves them to approximately 7.80277542266 and 12.1972245773. The middle50% interval keeps its width while changing center.

The ideal cumulative probability for zero location is 1/(1+EXP(-x/a)). At x=2*LN(3), it equals 0.75. This cross-check uses a fixed x and known formula; it is not a probability inferred from one changing D2 value.

For an ideal standard deviation 3, use scale =3*SQRT(3)/PI(), approximately 1.65398668627. Feeding 3 directly to RANDLOGISTIC would instead produce ideal standard deviation approximately 5.4413980927.

This conversion is useful when comparing a logistic error model with a normal model using the same standard deviation. Matching spread does not make their shapes or tail probabilities identical.

For nonnegative t, the ideal probability of ABS(X)>t is 2/(1+EXP(t/a)). With the original scale 2 and threshold6, the result is approximately 0.0948517463551. The complementary central probability is approximately 0.905148253645.

For the shifted D3 model, that central interval is 4 through 16. The threshold is three scales, not three standard deviations. Report both scale and the interpretation of the threshold instead of calling any multiple of the parameter a sigma rule.

=RANDLOGISTIC(0) gives 0 after an accepted finite driver; =RANDLOGISTIC(-2) gives #NUM!. There is no early-return zero-scale branch, so a zero result does not mean no generator state was used.

D3’s reference deliberately preserves the same draw. Separate calls do not share the same U by promise, and copying references to D2 does not create independent samples. For reproducible deterministic teaching controls, keep the supplied U column separate from the volatile result cell.

The function is registered as volatile. A recalculation can replace its result; neither a copied screenshot nor an earlier value is a promised next draw. There is no seed argument in this function’s worksheet signature. Exact recalculation triggers, shared-generator sequencing and saved-file replay were not tested.

The controls below separate a changing random formula from deterministic arithmetic. The supplied driver values are teaching inputs, not values captured from Gnumeric’s generator. Population summaries describe the ideal continuous distribution and are not empirical certifications of the finite-resolution implementation.

Use explicit finite numeric inputs for these controls. Text parsing, blank-cell coercion, locale-specific separators and array broadcasting are outside the verified examples. The numeric result constructor turns non-finite arithmetic into #NUM!; very large parameters or extreme transformed values can therefore fail even when the mathematical distribution is defined.

The underlying unit generator has finite resolution. Endpoint exclusions, rounding, overflow and underflow mean a theoretical continuous distribution is not a literal list of every machine output. No random samples, native worksheet execution, distribution-quality test, GUI operation or cross-application file transfer was performed for this guide. The executable checks verify deterministic transformations and mathematical reference values only.

• Function help and worksheet callback
• Pinned transformation helper, finite-resolution unit generator, and volatile registrations
• Finite-number result and error conversion
• Gnumeric official function catalogue

RANDLAPLACE, RANDCAUCHY.