Can you please advise which distribution to follow when your skewness is 0.28 and Kurtosis value is 51. Since it's leptokurtic and positively skewed I would like to fit distribution and also wanted to calculate distribution value at each time "t" just like we calculate Z score for Normal Distribution.
That can be a somewhat difficult question to answer, given that the context may yield different distributions. Nevertheless, I think that you could try to fit the best distribution algorithmically. For instance, lately I found this package at Matlab file exchange:
Finding the best distribution that fits the data Link
(...) This is where Mike's allfitdist comes into play. Statistics Toolbox supports a long list of distributions, including parametric and nonparametric distributions. allfitdist fits all valid parametric distributions to the data and sorts them using a metric you can use to compare the goodness of the fit. (...)
Hope that this helps. Let me know whether it worked for you!
I think the best answer is to test different distributions with your specific data set and see which fits the data the best... skewness and kurtosis are just a small piece of information , there is still a good deal of information we don't know and won't have with out having the data set in front of us