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I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g

data = {{0.338647979`, 0.872505848`}, {0.968996669`, 
0.719739697`}, {0.588260722`, 0.341745365`}, {0.067679752`, 
0.402356414`}, {0.865388685`, 0.473392859`}, {0.253667931`, 
0.567197392`}, {0.426197633`, 0.407360178`}, {0.177320994`, 
0.017256856`}, {0.951414021`, 0.982223584`}, {0.253667931`, 
0.786780701`}, {0.656580363`, 0.957540658`}, {0.036178408`, 
0.543456086`}, {0.951414021`, 0.677829855`}, {0.943068661`, 
0.829664051`}, {0.715070349`, 0.728622648`}, {0.90585328`, 
0.909677732`}, {0.838115922`, 0.950789948`}, {0.253667931`, 
0.893627494`}, {0.426197633`, 0.464786567`}, {0.656580363`, 
0.077545663`}, {0.338647979`, 0.398461231`}, {0.426197633`, 
0.394135461`}, {0.426197633`, 0.112919872`}, {0.114532957`, 
0.35637162`}, {0.764140605`, 0.313629714`}, {0.177320994`, 
0.094972012`}, {0.426197633`, 0.279514331`}, {0.338647979`, 
0.233104426`}, {0.426197633`, 0.454430193`}, {0.00714071`, 
0.028908663`}, {0.838115922`, 0.240920824`}, {0.656580363`, 
0.198827205`}, {0.253667931`, 0.187220634`}, {0.426197633`, 
0.739375201`}, {0.588260722`, 0.798031354`}};

dist = CopulaDistribution[{"Frank", \[Alpha]}}, {UniformDistribution[], UniformDistribution[]}]; 
d = EstimatedDistribution[data, dist]
m = DistributionFitTest[data, d]

The output is

CopulaDistribution[{"Frank", 0.0632689}, {UniformDistribution[{0, 1}], UniformDistribution[{0, 1}]}]

0.733126

and now I try another copula type

dist = CopulaDistribution[{"Clayton", c}, {UniformDistribution[], UniformDistribution[]}];
d = EstimatedDistribution[data, dist]
m = DistributionFitTest[data, d]

The output is

CopulaDistribution[{"Clayton", 1.61938}, {UniformDistribution[{0, 1}], UniformDistribution[{0, 1}]}]

0.733126

The goodness of fit value is the same even though I am using a different estimated distribution. I try other copulae but I get the same p-value of goodness of fit.

After that I attempted to find the goodness of fit test of data without any distribution as DistributionFitTest[data]: the p-value is 0.743417.

I also tried to give some arbitrary values to the copula distribution instead of Estimated distribution but the result were the same.

Whats wrong here?

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  • $\begingroup$ Try it without using estimate/arbitrary values, that is, feed it the distribution target with symbolic parameters. Otherwise, p-values can get whacky (in fact, try plotting the distribution of them and see what you get.) $\endgroup$
    – ciao
    Aug 19, 2015 at 10:27
  • $\begingroup$ @ciao Its bivariate case I think plotting is not good choice. $\endgroup$
    – SAAN
    Aug 19, 2015 at 10:37

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