# What defines a plateau in a saturation curve?

I am working on a dynamic visual. To be more specific, it is a saturation curve (also known as accumulative/cumulative curve that reaches to a maximum of 100%. I am trying to define a variable that measures when this curve gets to “plateau”. It could reach 99% with the first 5 data points and it could reach the top 85% at the top 100 points. Can you please help me with the right measure to define when the curve reaches “flat”? E.g. I am wondering if theres a statistic that gives a penalty like AIC/BIC for models to measure “flatness” Thank you

• Whatever the "right" measure might be is a matter of convention and your application. There is no universal statistical solution nor should there be--anyone claiming otherwise could do so only in ignorance of the range of possible applications. Please tell us, then, what your plateau measures and what the consequences might be of underestimating or overestimating the point at which it is arrived. – whuber Feb 8 at 12:58
• I simply have a long list of items that people could buy and I am trying to see which of these do not actually matter. I am looking for a measure like a Standard deviation that defines what a “spike” is. Similarly, i am looking for a measure that defines what “flat” is. Any thoughts? – Learner123 Feb 8 at 15:36
• There's no statistical answer to that, because "flat" is whatever you want it to be. It's unclear whether "flat," whatever it might mean, has anything to do with what matters to purchasers. It's hard to see how one could give a considered opinion about what the "right" measure of flatness might be. – whuber Feb 8 at 15:41
• Ok let me clarify a bit more. When there are 10000 product that people could buy from, a step of 1% in a saturation curve is a big deal, but when there are 10 items people could buy from, 1% is insignificant. Therefore i am looking for a formula that gives a smaller window for “flatness” with increased number of products. (Think of how AIC gives a penalty on an increased number of variables in a model, vs how the definition of “flatness” can change with increased number of datapoints) – Learner123 Feb 8 at 15:44