I have a collection of real-world samples that I am trying to model and then forecast.
There are 10 datasets – each has an increasing number of data points (from 1 to 10). The points are equi-distant and each has some percentage of the total allocation for that set. For example, the first set has 1 data point with 100% allocation; second has 2 points with 50% each, etc. The sets appear to have a roughly normal distribution – but with a small skew to the right of the curve.
As the number of data points increases with each set, the x-axis expands and the distribution is spread thinner over the set (ie. the mean decreases and the curve becomes more flat (lower kurtosis?)).
I am using MathNet Numerics for C#. I have tried importing one of the datasets into a normal distribution and having the library calculate the mean, SD, skew, kurtosis, etc.
Firstly, given those parameters for a normal distribution, is it possible to reproduce the values for a given number of data points? e.g. Can a normal distribution be divided equally on the x-axis and the percentage allocation for each point be calculated?
Secondly, given the sample datasets, is there any way to model or find a function for the change between the datasets so that I may forecast the distribution for any number of data points? (e.g. given the shape of the distribution for 5 and then 10 datapoints, what would the distribution be for 15 or 20?).
I am not a statistician, so please forgive me if I have asked something obvious or if anything doesn't make sense.