Consider a system whose output is a discrete random variable $X$ with probability mass function given by $p_t$. Here $t$ indicates that the distribution $p_t$of the random variable $X$ is a function of time (discrete). Suppose I have obtained a sequence (kind of a time series) of distributions corresponding to $X$, say $D= \{p_1,....,p_n\}$. How to find the best distribution $p_X$ that represents the random variable $X$ with respect to an appropriate metric?
Can someone guide me to some metric/results/frameworks in probability and statistics that address my problem?
I would suggest using recurrent neural network if you have enough data. look for relative entropy or KL distance it might help.