Looking for a bell curve formula to present data that has zero to full affect in a range

Question

a=(0-100)

when x=0, a should be 0 when x=100, a should be 100

the data needs to bell curve towards the 100 mark, so that once x passes 100 a will remain at 100 and not go over.

Explanation and application follows:

We have a number of rows of data that are counted as good, bad or questionable. If a row is bad we count it as full value (1.0) against the total. so 100 rows with o1 bad = 99% success if a row is questionable, we count it as a percentage of 1 against (maybe .75) so 100 rows with 1 questionable results in 99.25% success

I would like to build in a factor to apply to that value (bad affect or questionable affect) that would reduce it to zero affect (in either case) if there is only 1 row of data. so.. some thing like: 1 row with 1 bad or questionable = 100% success (no matter the questionable affect) 2 rows with one bad would yield nearly 100% success 10 rows with one bad might yield a 99% success rate 50 rows with 1 bad would yield 99.5% 100 rows with one bad would yield 99%

similar affect to questionable results

This factor that I am attempting to derive would be applied to the affect variable for each of bad and questionable affects.

The factor also will have no implication on the affect once it reaches a certain value, in the above sample 100. it will always start at 0.

Thanks for any assistance. -Scott

Answer 1

To fit an bell curve you will need two parameters. From data you provided, you can estimate only one parameter so to fit another you will be needing more data. eg. Lets say you want to fit a normal curve with (mean m , and variance v) then you can easily say your variance is 50 =(100-0/2) but you still cannot measure m. You can estimate m based on data you have and your requirements. Similary you can fit any other curve too. Given your use case weibull might be an better curve than normal as you dont want a symmetrical curve.

Secondly be it any curve it cannot fulfill the proposition that x should remain constant 100 for a>100. to achieve this you will have to use 2 or more equations to define enitre curve as

f(x) = 0 for x<= 0

   BellCurve(x) for 0<x<100

   100 for x>=100

Answer 2

Can a simple shape function do the job. Something like

y = 50-50*cos(PI*x/100)    if x>=0 & x<=100