Corpus ID: 235694686

On the distribution of the sum of dependent standard normally distributed random variables using copulas

  title={On the distribution of the sum of dependent standard normally distributed random variables using copulas},
  author={Walter Schneider},
The distribution function of the sum Z of two standard normally distributed random variables X and Y is computed with the concept of copulas to model the dependency between X and Y . By using implicit copulas such as the Gaussor t-copula as well as Archimedean Copulas such as the Clayton-, Gumbelor Frank-copula, a wide variety of different dependencies can be covered. For each of these copulas an analytical closed form expression for the corresponding joint probability density function fX,Y is… Expand

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