is there a Kalman filter for distribution function?

The standard Kalman filter uses a series of measurements observed over time, to decomposite the signal and noise.

However, when I'm modeling the distribution (pdf or cdf) of a variant, is there a similar tool?

For example, here's a random variable $X(month, PaymentDelay)$ describe how many days (PaymentDelay) people will pay the credit card bill after get informed.

This is a discrete variant valued on non-negative integer: $PaymentDelay \in [0,1,2, ...]$.

Each month there have an observation.

Define $\mu(month) = E(X(month,PaymentDelay))$, Kalman filter could be used to generate a more accurate estimation of $\mu$, to predict $\mu(month+1)$ from historical data.

However, if the target is the distribution $X$, is there a similar way to get an more accurate estimation on $\hat X(month+1, PaymentDelay)$ from historical observations?

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you might have better luck on cross validated, to be honest... –  Lost1 Mar 26 '13 at 16:48
@Lost1 oh never know there's such a stackexchange forum .... thx i'm moving it there... –  athos Mar 27 '13 at 3:41