Creating Fit Curve/Prediction Interval for Scalar output

I have some data for which I would like to create a 95% prediction interval, where I could say that 95% of the time the next observed data point will lie within the interval. From what I've found so far, I will need to create a fitted curve to my data and use that with nlpredci to find the interval (for non-linear cases). One thing I'm confused about is how to find a fitted curve. My data is a bunch of scalar values, so I only have one vector to input, not 2 (x and y) like it asks for. This is because I am basically performing a function multiple times that involves some randomness, so each value is unrelated to each other or to an independent variable. I would like to create an interval where if I performed the same function again I could predict its value.

Would it be cutting corners to say the 95% prediction interval is the interval from the 2.5 percentile and the 97.5 percentile of my data? Otherwise I'm not sure how to fit a curve to it.

Thanks!