For numerical simulation of statistical processes one uses algorithms to generate random numbers with a given distribution. A direct method to generate numbers x with a desired distribution is to put \(x=F^{-1}(u)\), where \(F^{-1}\) is the inverse of the cumulative distribution function and u is uniformly distributed on the unit interval, but this method needs acceptance rejection tests. An example is the normal distribution for the polar method to the case of exponential density.
In this paper the authors present an extension of the polar method to the case of exponential density of the form: \[ f_{\nu}(x)=C_{\nu}\exp (- \lambda | x|^{\nu}),\quad C_{\nu}=\nu \lambda^{1/\nu}/(2\Gamma (1/\nu)). \] An evaluation of the method presented here shows that its overall performance compares favorably with other standard alternatives as in speed and in precision, too.