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Suppose that I have a dynamic variable X that changes with time, and suppose that I know it's statistical distribution over a period of the last 10 years, and this dis. telling me that the most probable value for X is for example 90.

Now suppose that I have another statistical dis. of the same variable, but only for the last year (that is the it includes the previous dis.), and it tells me that most probable value for X is 100.

Obviously having two distributions means I have more information, and clearly the Dis. of last year shows that there is kind of a rising trend, that is why it is 100 not 90, but first Dis. also telling us that it is little bit far from the most probable value, so common sense telling me that most probable value should be somewhere in between 100 and 90, and my question is how to calculate it?

P.S I'm interested in the "joined" dis. as a whole, not just the most probable value. If the answer is long, pls just refer to some link or book or how this concept of joining is called in statistics.

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  • $\begingroup$ Can you tell us your application, that is, your context, what is the applied problem you are trying to solve? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jun 27, 2014 at 12:49
  • $\begingroup$ I Belive it's irelivant, but first what comes into my mind, is for example stock prices. $\endgroup$
    – TMS
    Commented Jun 27, 2014 at 13:27
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    $\begingroup$ TMS: In statistics, context is never irrelevant! $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jun 27, 2014 at 14:29
  • $\begingroup$ Ok, I just studied statistics and probability as an abstract, not applied field, that why I put my question in this way, anyway lets stick to my example, suppose it is stock prices. $\endgroup$
    – TMS
    Commented Jun 27, 2014 at 17:18
  • $\begingroup$ To see if the mean changes with time, you can search for "testing for structural change". There is an R package strucchange for this. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jun 27, 2014 at 17:22

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