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I have simulated data of a 4-dimensional random variable $(X_1,X_2,X_3,X_4)$. The individual pdfs of these random variables, i.e., $X_i$ where $i\in\{1,2,3,4\}$ turns out to be stable distributed with no mean and variance. Though I am able to use fitdist MATLAB COMMAND to fit these distributions to Weibull distribution and the marginals turn out to be more or less identical in terms of parameters.

My aim is to generate a copula so that I can use that interrelation rather than using the simulated data for further processing and calculations. For this I am using copulafit MATLAB Command but none of the given copula family there can simulate my data properly or even approximately.

The data that I am using is also not producing a simple bivariate correlation, it is somewhat like this: correlation data between any two random variable data Where should I seek help to generate such data, that can have correlation like as given in the figure.

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  • $\begingroup$ Maybe Mathematica's copulas have different options: reference.wolfram.com/language/ref/CopulaDistribution.html. If you need a parametric density, why not use a mixture distribution to approximate the underlying distribution? $\endgroup$
    – JimB
    Oct 9, 2023 at 21:10
  • $\begingroup$ What does the sample copula density look like? $\endgroup$
    – Glen_b
    Oct 9, 2023 at 22:48

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The shape of the univariate marginal distributions does not matter, as each one has to be transformed to Uniform[0,1] by the inverse CDF (the probability integral transform, PIT) before a copula is fit. For flexible multivariate copulas, try vine copulas. An automated algorithm of model building and selection of Disssmann et al. (2013) is implemented as function vinecop in the rvinecopulib package in R. Its building blocks are a rather wide range of bivariate copulas; perhaps some of those would fit your data. (Of course, this is not the only alternative.)

Reference: Dissmann, J. F., E. C. Brechmann, C. Czado, and D. Kurowicka (2013). Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59(1), 52-69.

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