How to use copula Distribution Parameter to Find Marginal Distributions?

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frankovaT 2018-11-19

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评论： Jeff Miller 2018-11-20

I have 2 time sereis of Precipitation and Temperature. I made a two dimensional copula distribution of them and I have the Estimated Correlated Parameter between them. Which is like:

Rho =
    1.0000    0.7220
    0.7220    1.0000

Now I want to use this Estimated Parameter, to estimate 2 Marginal distributions. I have a new Precipitation and I want to estimate the marginal temperature based on the precipitation I have.

It is important to note that new percipitation and new marginal should follow the same distribution function as wqas used to calculate corrolation parameter.

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Answer 1

Jeff Miller 2018-11-19

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I don't really know the answer to this, but it might help you to know that what you are looking for is called a "conditional" rather than a "marginal" distribution of temperature (for a given value of precipitation). Here is a relevant link, unfortunately for R, but maybe you can find the analogous thing for MATLAB: Conditional probability with copulas

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frankovaT 2018-11-20

No, I am afraid. I am talking about getting back to "marginal" distributions from a "Joint" distribution.

Jeff Miller 2018-11-20

Hmmm, if you are really just interested in the marginal distributions, then the correlation parameter given in your original question is irrelevant. Did the fitting program give you some parameter estimates for the marginal distributions? Those define the marginal distributions directly; the Rho parameter is only relevant in indicating the bivariate (correlation) structure of the two variables with those marginals.

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