Abstract
In this paper, we propose a simple method to generate generalized Gaussian noises using the inverse transform of cumulative distribution. This inverse is expressible by means of the inverse incomplete Gamma function. Since the implementation of Newton's method is rather simple, for approximating inverse incomplete Gamma function, we propose a better and new initial value exploiting the close relationship between the incomplete Gamma function and its piecewise linear interpolant. The numerical results highlight that the proposed method simulates well the univariate and bivariate generalized Gaussian noises.
Highlights
The study and application of univariate and multivariate generalized Gaussian distributions (GGD) is an active field of research in theoretical and applied statistics
The generation of multivariate distributions has not been investigated extensively and we have not enough literature on Monte Carlo techniques for synthesizing multivariate random processes, except from the work done by Johnson [14]
We show that the numerical quadratures for weakly singular integrals by nonlinear spline approximations proposed in [15], is efficient for computing numerically P (a, x)
Summary
The study and application of univariate and multivariate generalized Gaussian distributions (GGD) is an active field of research in theoretical and applied statistics. We are going to use classical Monte carlo procedure to simulate sampling from Gamma distribution In this case, we should invert incomplete Gamma function. In [12], the analytical approach from earlier literature is summarized and new initial estimates are derived for starting the fourth order Newton method. This method is not, as flexible as is desirable because the starting values need: dividing the domain of computation, Taylor expansion, continued fraction, uniform asymptotic expansion, asymptotic inversion, inversion of the complementary error function.
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