POISSON Function (Gnumeric)

• Introduced: First release not established; this name is present in the tested Gnumeric 1.12.57 and the cited 1.12.62 source.
• Availability: Supported in Gnumeric 1.12.62 according to its function-specific registration. No retirement endpoint is established.
• Scope: Desktop Gnumeric with the fn-stat module enabled. Examples use English comma-separated formulas.
• Checked: October 14, 2026. Reference and boundary tables were recalculated by Gnumeric 1.12.57 and checked independently. The 1.12.62 contract was source-checked, not executed.

For mean λ>0, the mass at integer x is exp(−λ)λ^x/x!. Cumulative mode sums this mass from 0 through x. The model has equal mean and variance and assumes an appropriate constant-rate independent-event process; the function does not establish those assumptions from a count. Official POISSON reference.

=POISSON(x,mean,cumulative)

All arguments shown are required. Use numeric cells or numeric inputs. The formulas use decimal points and commas; localized entry conventions require separate checks. Gnumeric 1.12.62 help and evaluator.

Enter each formula in a separate cell. The displayed references are rounded to twelve decimal places and agree with the recorded Gnumeric 1.12.57 recalculation within ordinary floating-point precision. Keep the stored result for subsequent calculations.

Suppose a model expects three arrivals during a specified interval. Put count 2 in A2 and mean 3 in B2. =POISSON(A2,B2,FALSE()) gives approximately 0.224041807655, the chance of exactly two arrivals. =POISSON(A2,B2,TRUE()) gives approximately 0.423190081127, the chance of at most two.

Use a mean for the same interval as the count. A rate of six arrivals per hour corresponds to mean 3 in half an hour under the constant-rate model.

Calculate “at least” without losing one count

The probability of at least three events is =1-POISSON(2,3,TRUE()), approximately 0.576809918873. Subtracting POISSON(3,3,TRUE()) would instead give the probability of at least four. Write the desired inequality beside the cell.

The probability of zero arrivals during the half-hour interval is =POISSON(0,3,FALSE()), approximately 0.049787068368. This agrees with EXP(−3), providing a simple independent special-case check. For very tiny upper tails, subtracting a value rounded near 1 can lose relative accuracy.

Gnumeric requires mean>0: mean=0 returns #NUM!, even though a mathematical degenerate Poisson distribution can be defined at zero. Do not copy another spreadsheet’s zero-mean output. Event counts are floored before the nonnegative guard, so −0.1 is rejected rather than treated as zero. Use integer counts. All three arguments are required.

The following are observed cell results from the same 1.12.57 command-line recalculation. F5 was genuinely empty. A blank is not necessarily an omitted argument or a valid observation, so validate required data instead of treating every defaulted zero as intentional.

The fixtures do not certify every locale, extreme tail, imported type or newer binary build. The current wrapper agrees with the documented argument contract; shared numerical helpers can change between releases.

• BINOMDIST
• NEGBINOMDIST
• POISSON official manual entry
• Version-pinned argument contract and calculation