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priori unknown. A Gaussian-like exponential function 

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was chosen, which was confirmed by high energy synchrotron x-ray diffraction measurements $^{23}$. Since α is restricted to [0 , 90 $^{◦}$], the density distribution function has to be renormalized numerically 22 and is formally not a true Gaussian distribution. This implies that α$_{t}$ is no longer the standard deviation of the distribution or an average misalignment angle, which are restricted to angles below 90 $^{◦}$, but only a parameter which characterizes the decrease of the density distribution function between 0 and 90 ◦ and, therefore, the degree of texture. α$_{t}$ converges to zero in the limit of perfect texture and diverges in untextured materials ( f$_{a}$ becomes constant between 0 and 90 ◦ for α$_{t}$ → ∞ , uniform distribution). 

Only a few quantitative data about texture in MgB$_{2}$ tapes exist in the literature, varying between 20 ◦ and 30 ◦ $^{5,23}$, but the model is not restricted to this angular range. For α$_{t}$ → 0 and ∞ , the results of the model merge the predictions of the anisotropic scaling approach 35 and the percolation model for untextured MgB$_{2}$ $^{14}$, respectively. 

For the calculation of the angular dependence of J$_{c}$ , B$_{c2}$ and B$_{ρ}$$_{=0}$ , the density distribution function with respect to the direction of the applied magnetic field is needed, which was derived from the distribution function Equ. 1 in Ref. 22. All following calculations are based on this density distribution function. 

## III. RESULTS AND DISCUSSION 

At first we focus on the anisotropy of the zero resistivity (irreversibility) field B$_{ρ}$$_{=0}$ . This quantity is less model dependent than J$_{c}$ . It is independent of the pinning mechanism, the transport exponent and anisotropic scaling. Only the angular dependence of the upper criti- cal field has to be known. Good agreement with the theoretical prediction of the anisotropic Ginzburg Landau theory $^{36}$, 

was demonstrated $^{10,13,37,38}$. It was shown in Ref. 16, that B$_{ρ}$$_{=0}$ in untextured materials is given by ab 

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