Math Moron here in need of a function to simulate a degrading curve over time.

I am trying to find a function to simulate the curve found in this arbitrary data. The use case is bringing a score to zero over a given time similar to the positive side of a normal distribution. I am hoping for two variables, increments of time and score, that at a given time the calculation could be made and the new degraded, lower, score would be returned. I have tried hard to make the guassian distribution probability function work but if it can I just don't have the chops to figure it out. I went down some other rabbit holes including degredation kinetics equations, parametric degredation, and learned that the Taylor series is really cool but not able to help me. All of which are out of my depth.

Here is the curve I am trying to find a function for.

I could not figure out how to make a table in this UI so I am providing a link to a google sheet. The data is arbitrary but approximates the curve I am looking for.

https://docs.google.com/spreadsheets/d/1SodshwZrKrBTgEdQnn7kHuO-chAEuDKZyS1qOtAztf8/edit?usp=sharing

I admittedly suffer from such a low understanding of higher math that I don't even know the best terms to research. I appreciate any help or even direction towards help that can be offered.

Thank you for your time,

Bill

Answer 1

[Mathieu NOE]

hello

maybe this ? (the idea behind is a sigmoid)

samples = 100;
c = samples/2; % center of the curve (c corresponds to the x value where y = 0.5)
x = (0:samples-1)';
a = 0.15; % define how sharp is the transition
y = 1 - 1./(1 + exp(-a.*(x-c)));

plot(x,y);

[Mathieu NOE]

maybe I was a bit too quick

are you looking for a curve that ressembles or that really fits the excel data ? if the second answer is the right one then you can try polyfit

[Bill Bozarth]

Thank you Mathieu

That is a great curve for what I need. Give me a minute to try to understand it.

[Bill Bozarth]

Thank you a bunch Mathieu! Perfect answer!

[Mathieu NOE]

as always, my pleasure !