OBD talk:BINA/PAR3

To value types:

What the both values of the normal distribution stand for?

First value μ (mean) and second value σ (standard deviation)?

Ssg 23:13, 5 December 2007 (CET)

No as far as I can tell. The value is interpolated from an "InverseNormalTable" (0, 0.125, 0.2533, 0.3850, 0.5244, 0.6745, 0.8416, 1.0364, 1.2816, 1.6449, 3.0902, 1.6449, 1.2816, ...). The resulting value is multiplied with the second value and the first value is added to the result, so those 2 value are more like "offset" and "scale". I don't know why the table is called "InverseNormal", maybe this is actually normal inverse distribution but it does not look like so.

Neo

Thanks for your answer.

I've googled a (long) bit for that "InverseNormalTable". It seems to be okay. This table is also called "inverse standardized normal distribution" (see http://files.hanser.de/hanser/docs/20040419_24419112747-75_3-446-21594-8Anhang2.pdf)

The equation for the inverse normal distribution is: x = σ * z + μ

with:

x = result

z = looked up in the z-table (the z-table here is the InverseNormalTable)

μ = mean

σ = standard deviation

Unfortunately I've no idea what's the basis for Oni's interpolation (IMO Oni needs an entry point for the table), so I haven't got a clue what the result is for.

Ssg 20:26, 6 December 2007 (CET)

The interpolation is easy: it picks a random number between -9.99 and 9.99 and it uses it to interpolate the table (linear interpolation).

And I don't know if you noticed, the WMDD for values says "Bell Curve" :)

Neo

A quick note: I messed up the table, it's (-3.0902, ..., -0.2533, -0.125, 0, 0.125, 0.2533, 0.3850, 0.5244, 0.6745, 0.8416, 1.0364, 1.2816, 1.6449, 3.0902).

Neo

>>it picks a random number between -9.99 and 9.99 and it uses it to interpolate the table (linear interpolation).

I don't get that. Can you give an example, please? Let's say Oni picks up the value 9. How does the interpolation work?

Like this:

-3.0902 = -9.99

-1.6449 = -8.99

...

-0.125 = -0.99

0 = 0

...

3.0902 = 9.99?

>>And I don't know if you noticed, the WMDD for values says "Bell Curve" :)

Yes, I've noticed that. Do you think the first value is not the mean?

>>I messed up the table

No problem. Now it fits much better to the pdf file above. ;-)

Ssg 22:32, 6 December 2007 (CET)

This should clear up everything:

float InverseNormalTable[] = { 0.0f, 0.125f, 0.2533f, 0.3853f, 0.5244f, 0.6745f, 0.8416f, 1.0364f, 1.2816f, 1.6449f, 3.0902f };

float InverseNormalRandom(float v1, float v2)
{
    float r = frnd(); // generates a random number in [-0.999, 0.999]
    float x = fabsf(r) * 10.0f;
    int i = floorf(x);
    float z = InverseNormalTable[i] + (x - i) * (InverseNormalTable[i + 1] - InverseNormalTable[i]);

    if (r < 0.0f)
        z = -z;

    return v1 + z * v2;
}

Neo