Alternate forms for numerical evaluation of cumulative probability distributions directly from characteristic functions
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Alternate integral forms for the cumulative probability distribution in terms of the characteristic function are given. In particular, forms that can utilize a fast Fourier transform algorithm and special forms for one-sided probability density functions are derived. For a special class of discrete random variables, all integral evaluations are over a finite range.
[1] J. Cooley,et al. Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals , 1967, IEEE Transactions on Audio and Electroacoustics.
[2] A. H. Nuttall. Numerical evaluation of cumulative probability distribution functions directly from characteristic functions , 1969 .