Goodness of Fit of Copula Distribution

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?

• 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.)
– ciao
Aug 19, 2015 at 10:27
• @ciao Its bivariate case I think plotting is not good choice.
– SAAN
Aug 19, 2015 at 10:37