# Weighted distribution of Numbers

Douglas Ruisaard dougr at telus.net
Mon Aug 5 11:50:41 EDT 2019

```Ralph:
Although several persons have responded... most far above my "pay-scale" ... Your mention of the audio taper rang bell for me.  In the process of simulating an analog audio potentiometer using a digital one... I needed to find a formula for an inverse audio taper... and it DID take a math professor to finally provide a solution:

kx - 1 + sqrt((1 - kx)^2 + 4kx^2)

y = ---------------------------------

2kx

Now referencing the potentiometer "model"...
"x" is the amount of "rotation" .. from near zero (since dividing by zero is verboten) to 100%.. i.e. 360 degrees (which a real analog pot never actually achieves.
"k" is the "weight" factor ... increasing "k" increases the "severity" of the taper ... more or less flattening the higher range which, in turn, causing the "higher" rotation values to have less differentiated output values
"y" is the output ... in the case of a pot, the resistance

When I look at the graph of this function using a "k" value of 5 and above, I *thinK* it starts to simulate your desired mapping.

Hope this helps ... quadratic formulae are NOT my thing.  Your mission is to fit this formula into you app and data set

Cheers!
Douglas Ruisaard
Trilogy Software
(250) 573-3935

>
> Message: 12
> Date: Sun, 4 Aug 2019 14:49:09 -0400
> From: "Ralph DiMola" <rdimola at evergreeninfo.net>
> To: "'How to use LiveCode'" <use-livecode at lists.runrev.com>
> Subject: [OT] Weighted distribution of Numbers
> Message-ID: <003701d54af5\$4f8cd410\$eea67c30\$@net>
> Content-Type: text/plain;	charset="us-ascii"
>
> I have a set of raw numbers(6,000 of them from 0 to 800 or so). It was easy
> to normalize these numbers from 0 to 100. But as I look at the results I see
> that there is one at to top(100) and a few in the 90s and many more in the
> 70s and 80s. I need to make these numbers more evenly distributed and
> weighted towards the top(so the top few are 100) based on the current
> distribution of the raw numbers. I'm not a math whiz and not afraid to admit
> that going beyond linier equations is way over my head. From some searches I
> see the some sort of nonlinear regression is in order(I think)? Or a apply a
> log (like an audio log taper of a potentiometer)? I don't know... Can anyone
> point me in the in the right direction?
>
> Thanks!
>
> Ralph DiMola
> IT Director
> Evergreen Information Services
> rdimola at evergreeninfo.net
>
>
>
>

```