LOGNORMDIST

What it does

LOGNORMDIST(x, mean, standard_dev)

LOGNORMDIST(x,mean,standard_dev) returns the probability that a positive lognormal variable is no greater than x. Its mean and standard deviation arguments describe ln(X), not X. This legacy function always returns a cumulative probability; it has no density switch.

Try it

=LOGNORMDIST(1,0,1) returns 0.5: ln(1) is the centre of the specified normal distribution. With the same positive spread, values below one have probabilities below one half and values above one have probabilities above one half.

=LOGNORMDIST(EXP(1),1,0.5) is approximately 0.5. Mathematically, the median is exp(mean); in a worksheet composition, the stored EXP result and the later logarithm can introduce their own rounding.

Quirks

Nonpositive x or nonpositive standard deviation gives #NUM!; nonnumeric arguments give #VALUE!. A negative log-space mean is allowed. All three arguments are required, and adding a fourth cumulative flag does not turn this spelling into LOGNORM.DIST.

The two tails are asymmetric in the original units even though ln(X) is normal. A CDF near one can round to one, so subtracting it from one may lose a small upper-tail probability. The standardization must use the log-space parameters, not statistics calculated directly from untransformed observations.

How to implement

The current shared kernel performs these steps:

1. Validate positive finite x and positive finite sigma.
2. Obtain the internal CRT logarithm L=crt_log(x).
3. Store the ordinary binary64 subtraction and division z=(L-mean)/sigma.
4. Evaluate the shared standard-normal CDF at z.

At x=1,mean=0, the logarithm and standardized value are zero and the CDF is one half. The standard-normal CDF has its own stored argument transformation and complementary-error dependency; its upper ERFC body remains open.

The code retains a 45-control public-composition observation on the modern spelling, but a later larger bank distinguishes the internal CRT log from worksheet LN at a named control. Thus NORM.DIST(LN(x),mean,sigma,TRUE) is a useful mathematical composition, not permission to replace the internal log on every input. This wrapper is shared by the current legacy implementation; the modern observation alone does not measure every legacy call.

Rust code

10 lognormdist "LOGNORMDIST" (3, 3) [V "x", V "mean", V "standard_dev"] |s, a, sv| {
    let [x, m, sd_] = nums::<3>(s, a)?;
    out(s, nl::lognorm_dist_kernel(x, m, sd_, true))
}

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

LOGNORM.DIST is the modern spelling. NORM.DIST describes the normal variable in log space.

Named variants

No named variants are recorded yet.