Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A random vector X with given univariate marginals can be obtained by first applying the normal distribution function to each coordinate of a vector Z of correlated standard normals to produce a vector U of correlated uniforms over (0,1) and then transforming each coordinate of U by the relevant inverse marginal. One approach to fitting requires, separately for each pair of coordinates of X, the rank correlation, r(ρ), or the product-moment correlation, rL(ρ), where ρ is the correlation of the corresponding coordinates of Z, to equal some target r*.  prove the existence and uniqueness of a solution for any feasible target, without imposing restrictions on the marginals. For the case where r(ρ) cannot be computed exactly because of an infinite discrete support, the relevant infinite sums are approximated by truncation, and lor and upper bounds on the truncation errors are developed. With a function r˜(ρ) defined by the truncated sums, a bound on the error r(ρ*) − r* is given, where ρ* is a solution to r...
['Athanassios N. Avramidis']
I am writing a research paper on a idea Constructing Discrete Unbounded Distributions with Gaussian-Copula Dependence and Given Rank Correlation
[{"from": "human", "value": "I am writing a research paper on a idea Constructing Discrete Unbounded Distributions with Gaussian-Copula Dependence and Given Rank Correlation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A random vector X with given univariate marginals can be obtained by first applying the normal distribution function to each coordinate of a vector Z of correlated standard normals to produce a vector U of correlated uniforms over (0,1) and then transforming each coordinate of U by the relevant inverse marginal. One approach to fitting requires, separately for each pair of coordinates of X, the rank correlation, r(\u03c1), or the product-moment correlation, rL(\u03c1), where \u03c1 is the correlation of the corresponding coordinates of Z, to equal some target r*.  prove the existence and uniqueness of a solution for any feasible target, without imposing restrictions on the marginals. For the case where r(\u03c1) cannot be computed exactly because of an infinite discrete support, the relevant infinite sums are approximated by truncation, and lor and upper bounds on the truncation errors are developed. With a function r\u02dc(\u03c1) defined by the truncated sums, a bound on the error r(\u03c1*) \u2212 r* is given, where \u03c1* is a solution to r..."}]