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In this paper, we study on improving the goodness-of fit for the data by using  τ -preserving transform for the semiparametric family of bivariate copulas. We estimate the generator functionusing the Bézier polynomial function and define  τ - preserving transformation on the generator function under positive quadrant dependence assumption. We investigate the performance of our methodology on real data example contained life expectancy study. The findings indicate that the model fitting is improved by using  τ - preserving transformation.

A goodness-of fit improvement based on τ -preserving transformation for semiparametric family of copulas