Which probability distribution favors the most recent data?

Question

I know that Gaussian (Normal) distribution has two parameters (mean and variance) which are updated with every new data point. But in the Normal distribution, the old data have a similar effect on the distribution as the newer data.

I have seen a number of other distributions (like Gamma, Chi-squared, Erlang, ...) which have a skewness property. I am not sure if the skewness can have anything to do with the age of the data points.

My question is:

Is there a distribution that favors the most recent data points (as opposed to the Normal distribution which doesn't consider the age of each data point)?

Answer 1

If the observations are iid, no matter the distribution, no. If we have something like a time series, where the correlation between observations is dependent upon the length of time between them, or if the variance of more recent observations is less, the answer is yes.