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RANDNORMTAIL Function (Gnumeric)

Statistical Intermediate Gnumeric

Draw from the upper tail of a zero-mean normal distribution in Gnumeric using a lower cutoff and standard deviation, with reproducible support checks.

Verification status: See the evidence and test scope described in this guide. How formula examples are checked

RANDNORMTAIL draws from the upper tail of a zero-mean normal distribution, restricted by a lower cutoff. It does not return the probability of exceeding that cutoff. Use a probability-distribution function for a tail probability and this function for a random observation conditional on being in the selected tail.

Syntax and arguments

=RANDNORMTAIL(a,sigma)

a is the lower cutoff in the same units as the desired result. sigma is the standard deviation of the underlying zero-mean normal distribution and must be positive for the intended model. Both arguments are required; there is no mean, seed or sample-count argument.

The source uses a direct rejection method for smaller standardized cutoffs and a specialized tail method for larger ones. That implementation choice is internal: users should specify the model in consistent units rather than adjusting parameters to select an algorithm branch.

Reproducible support checks

=RANDNORMTAIL(2,1) returns a random tail value, so no particular decimal is guaranteed. The bounded native fixture instead checks =RANDNORMTAIL(2,1)>=2, expected TRUE. A second control =RANDNORMTAIL(0,1)>=0 is also expected TRUE. These verify support constraints for individual draws; they are not a statistical test of the complete sampling distribution.

For a worksheet example, put 2 in A2 as the cutoff and 1 in B2 as sigma, then use =RANDNORMTAIL(A2,B2) in C2. Put a label explaining that C2 is a conditional random draw above the cutoff. The underlying normal mean remains 0; the tail-conditioned distribution has a different center.

Independently, the conditioning rule removes observations below a. It does not mean “add a to an ordinary normal draw”: adding a shifts the distribution but still allows values below a. That simple distinction can prevent a common simulation-model error.

Advanced use: units and thresholds

For a model with a nonzero mean mu, an explicitly derived transformation can use mu + RANDNORMTAIL(cutoff−mu,sigma), where all quantities share units. This construction describes a shifted model; it is not an extra undocumented argument to RANDNORMTAIL. Check that the underlying modeling assumption is appropriate before simulating.

If the cutoff is many standard deviations from zero, this is a rare region of the unconditioned normal distribution, but every returned draw is conditioned to be in that region. The number of tail draws you request says nothing about how frequently the original process crosses the cutoff.

Errors, reproducibility and history

Use positive sigma. The retained helper returns a non-finite value for sigma≤0, but invalid-sigma worksheet error presentation was not executed here and is not promised. Extremely large cutoffs or tiny scales were not tested; use bounded, meaningful parameters and inspect numerical warnings or errors.

Random results can change with recalculation and the function has no seed argument. Preserve a reviewed simulation realization as values when needed, while keeping the formulas and parameters separately. Do not certify a generator from two support checks.

The exact RANDNORMTAIL spelling is registered in retained 1.12.62 source and tested in 1.12.57. NEWS records an earlier RANDGAUSSIANTAIL name in 1.1.7, but this guide does not infer when the current spelling was introduced or declare the names fully interchangeable. Last functioning release remains unverified.

Native verification

Both native 1.12.57 support checks returned TRUE in one recorded execution. This establishes those bounded observations only, not a proof about all future draws.