Good afternoon everybody,

all my apologies if this is a stupid question and sorry in advance because I am sure I will not do a good job in explaining my problem, since it is not entirely clear to me either. Here it is. Suppose I have an unknown multidimensional probability density distribution

f(x_{1},\dots,x_{n})

but I know all the univariate marginal distributions

f_{i}(x) = \int{f(x_{1},\dots,x_{n}) dx_{j,j \neq i}}

and I have a constraint

g(x_{1},\dots,x_{n})=0

I know I cannot reconstruct f, since there is probably a family of f's that satisfy these conditions. However I would like to know whether it is possible to characterize this family of functions and, under specific conditions, find the functional form of at least one candidate that would satisfy the above constraints.

Thanks in advance for any help or pointer to literature or brilliant idea or simply interested comment.

Best regard,

Federico

all my apologies if this is a stupid question and sorry in advance because I am sure I will not do a good job in explaining my problem, since it is not entirely clear to me either. Here it is. Suppose I have an unknown multidimensional probability density distribution

f(x_{1},\dots,x_{n})

but I know all the univariate marginal distributions

f_{i}(x) = \int{f(x_{1},\dots,x_{n}) dx_{j,j \neq i}}

and I have a constraint

g(x_{1},\dots,x_{n})=0

I know I cannot reconstruct f, since there is probably a family of f's that satisfy these conditions. However I would like to know whether it is possible to characterize this family of functions and, under specific conditions, find the functional form of at least one candidate that would satisfy the above constraints.

Thanks in advance for any help or pointer to literature or brilliant idea or simply interested comment.

Best regard,

Federico

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