I would like to calculate the distribution (e.g., Gaussian) of a set of samples. However, I would also like to see how the distribution changes as I fit the samples into the distribution incrementally.
One way to do this would be to compute the distribution over all relevant samples every increment (e.g., first increment: calculate distribution of 2 samples, second increment: calculate distribution of 3 samples). However, this is computationally intensive.
Would I be able to calculate the distribution of 3 samples from solely the 3rd sample and the properties of the distribution of 2 previous samples?
For example, say I have 5 ordered samples.
- I start off by calculating the mean and standard deviation of the first 2 samples This is the 1st Gaussian distribution.
- I then look at the third sample, and fit it into the first Gaussian distribution (knowing the mean, std, number of samples). This is the 2nd Gaussian distribution.
- I then look at the fourth sample, and fit it into the 2nd Gaussian distribution (knowing the mean, std, number of samples). This is the 3rd Gaussian distribution.