The distribution of the weighted moving median of a sequence of iid observations

This paper provides a method for calculating or estimating the sequence of marginal distributions for a weighted moving median of a sequence of independent and identically distributed random variables. The particular example considered in detail is that of the exponentially weighted moving median, a robust alternative to the exponentially weighted moving average. For sample sizes up to N = 40 the marginal distribution can be derived exactly for any underlying distribution. For sample sizes greater than N = 40, simulation provides a useful method for calculating the distribution.