Method 1: Calculating the percentiles, e.g. 99 percentile of the data, is straight forward, and the calculation is based on the ordering of the data values.
Method 2: A more complicated way of calculating the percentiles will be first fit a distribution to the data (e.g. if we know the data is normal, we fit a normal distribution, or do a non-parametric Kernel density estimation), and then calculate the inverse cdf to get the 99 percentile of the data.
I am wondering is there any advantage for doing the latter method? My two guesses
- I am thinking inferring the percentiles from the distribution may be more robust as method 1 result is more sensitive to changes in the data?
- We can treat method two result as also a probability of the value occurring, whereas method 1 we can't?