[Libreoffice-bugs] [Bug 71109] NORMDIST() gives a percent result instead of a probability

[bugzilla-daemon at bugs.documentfoundation.org]

https://bugs.documentfoundation.org/show_bug.cgi?id=71109

--- Comment #10 from Eike Rathke <erack at redhat.com> ---
Our implementation here returns the ~same values as Gnumeric and probably Excel
as well. The returned values are NOT a percentage (you'll get different values
with different parametrization, e.g. multiply all X values and average and
standard variation by 0.1 and you'll see results multiplied by 10).

Note that Excel nowadays calls this Probability Mass Function instead of
Probability Density Function (the difference is function for discrete values vs
continuous values hence statistically more correct in this context, as the
probability of any one value out of continuous values is always zero), older
and derived documentation talk of density.

See
https://support.office.com/en-US/article/NORMDIST-function-126DB625-C53E-4591-9A22-C9FF422D6D58
also for the mathematical formula that is defined the same in
https://docs.oasis-open.org/office/v1.2/os/OpenDocument-v1.2-os-part2.html#NORMDIST
and also given at
https://en.wikipedia.org/wiki/Probability_density_function#Families_of_densities

You can easily check column B values with (here in R1C1 address notation)

  =EXP(-(((RC1-R1C3)^2)/(2*R2C3^2)))/(SQRT(2*PI())*R2C3)

Specifically note in that Wikipedia article's section the mention of "the
normalization factor of a distribution (the multiplicative factor that ensures
that the area under the density—the probability of something in the domain
occurring— equals 1). This normalization factor is outside the kernel of the
distribution."

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