WEIBULL Function (Gnumeric)

• Introduced: Documented by 1.12.62; original introduction not established.
• Availability: Supported in Gnumeric 1.12.62, based on the function-specific registration.
• Scope: Desktop; the fn-stat function module must be included and enabled.
• Checked: October 14, 2026. Official source and independent mathematical examples checked; Gnumeric 1.12.62 was not run.

WEIBULL evaluates a Weibull lifetime distribution. Shape controls how its modeled hazard changes, while scale sets the measurement units. The final Boolean chooses a cumulative probability or a probability-density value. Official function reference.

Let u=(x/beta)^alpha. For x>0 the CDF is 1−exp(−u), the survival probability is exp(−u), and the density is (alpha/beta)(x/beta)^(alpha−1)exp(−u). At x=beta the cumulative probability is 1−e⁻¹, about 63.21%, for every positive shape.

=WEIBULL(x,alpha,beta,cumulative)

Every argument shown is required. Use numeric inputs or cell references. The examples follow English Gnumeric’s comma-separated notation and decimal points; localized separators can differ. Release-pinned argument help and evaluator.

Enter each formula in an unused worksheet cell. These are independently calculated mathematical reference values rounded to twelve decimal places. Keep full stored precision in later formulas rather than retyping a rounded display.

Evaluate a lifetime threshold

For shape 2 and scale 4 hours, =WEIBULL(3,2,4,TRUE()) has expected cumulative probability 0.430217175269. The corresponding density =WEIBULL(3,2,4,FALSE()) is approximately 0.213668559274 per hour, which is not a point probability.

Compute an interval or percentile

=WEIBULL(4,2,4,TRUE())-WEIBULL(1,2,4,TRUE()) gives the modeled probability between hours 1 and 4. To find the 90th percentile, calculate =4*(-LN(1-0.9))^(1/2), approximately 6.069708517541 hours. Shape and scale must remain fixed across comparisons.

The release wrapper rejects x<0, alpha≤0 or beta≤0 with #NUM!. Zero-age density needs special care: for alpha<1 the mathematical density diverges; the helper returns infinity and the shared numeric constructor maps nonfinite output to #NUM!. For alpha=1 the mathematical density at zero is 1/beta; for alpha>1 it is zero. The ordinary positive-x table avoids this singular boundary. Pinned evaluator. Zero-age Weibull density. Nonfinite numeric result handling.

Shape 1 reduces the Weibull model to an exponential distribution with rate 1/beta. Thus =WEIBULL(3,1,2,TRUE()) and =EXPONDIST(3,0.5,TRUE()) have the same expected result 0.776869839852. For shape above 1 the modeled hazard increases with age; below 1 it decreases. These are model properties, not claims about any measured equipment.

EXPONDIST.

• WEIBULL manual entry
• Gnumeric 1.12.62 argument contract and calculation
• Zero-age Weibull density
• Nonfinite numeric result handling