In previous threads, it was mentioned that noise with a Gaussian distribution could be quickly approximated by summing 12 uniform RNG's. Is there an low overhead algorithm to generate samples whose distribution approximates a fat-tailed, extreme kurtosis, Pareto, or power-law decay distributions? This would seem to be useful when simulating or testing filters against noise sources thought to be more turbulent or chaotic than uniform or Gaussian. Thanks, rhn A.T nicholson d.0.t C-o-M

# "fat-tailed" pseudo-random number generation algorithm?

Started by ●April 25, 2007

Posted by ●April 26, 2007

Ron N wrote:> In previous threads, it was mentioned that noise with > a Gaussian distribution could be quickly approximated > by summing 12 uniform RNG's. > > Is there an low overhead algorithm to generate samples > whose distribution approximates a fat-tailed, extreme > kurtosis, Pareto, or power-law decay distributions?The extremely heavy-tailed Cauchy distribution can be generated by using the ratio of two zero-mean Gaussian rv's. Other ratios can be used as well, generally resulting in heavy-tailed distributions: http://en.wikipedia.org/wiki/Ratio_distribution> > This would seem to be useful when simulating or > testing filters against noise sources thought to be > more turbulent or chaotic than uniform or Gaussian.Turbulence and chaos are not modeled well using iid processes, regardless of the distribution. The characteristic behaviour of certain chaotic "time" series (stocks, sunspots, climatological phenomena, DNA patterns, music, serial chemical and physical measurements, humain gait patterns, you name it) is modeled using long- range correlations. Long-range correlated stochastic processes have auto-correlation functions which are not summable (resulting in a pole at DC in the PSD). The long ago past influences the far future. "long range correlation" seems to be a good starting point at Google. Regards, Andor

Posted by ●April 26, 2007

Ron N. wrote:> In previous threads, it was mentioned that noise with > a Gaussian distribution could be quickly approximated > by summing 12 uniform RNG's. > > Is there an low overhead algorithm to generate samples > whose distribution approximates a fat-tailed, extreme > kurtosis, Pareto, or power-law decay distributions? > > This would seem to be useful when simulating or > testing filters against noise sources thought to be > more turbulent or chaotic than uniform or Gaussian. > > > Thanks, > > rhn A.T nicholson d.0.t C-o-M >Look for the Matlab/Octave function called 'starnd'. John

Posted by ●April 26, 2007

Ron N. wrote:> In previous threads, it was mentioned that noise with > a Gaussian distribution could be quickly approximated > by summing 12 uniform RNG's. > > Is there an low overhead algorithm to generate samples > whose distribution approximates a fat-tailed, extreme > kurtosis, Pareto, or power-law decay distributions? > > This would seem to be useful when simulating or > testing filters against noise sources thought to be > more turbulent or chaotic than uniform or Gaussian. > > > Thanks, > > rhn A.T nicholson d.0.t C-o-M >Look for the Matlab/Octave function called 'starnd'. John

Posted by ●April 26, 2007

Ron N wrote:> In previous threads, it was mentioned that noise with > a Gaussian distribution could be quickly approximated > by summing 12 uniform RNG's. > > Is there an low overhead algorithm to generate samples > whose distribution approximates a fat-tailed, extreme > kurtosis, Pareto, or power-law decay distributions?The extremely heavy-tailed Cauchy distribution can be generated by using the ratio of two zero-mean Gaussian rv's. Other ratios can be used as well, generally resulting in heavy-tailed distributions: http://en.wikipedia.org/wiki/Ratio_distribution> > This would seem to be useful when simulating or > testing filters against noise sources thought to be > more turbulent or chaotic than uniform or Gaussian.Turbulence and chaos are not modeled well using iid processes, regardless of the distribution. The characteristic behaviour of certain chaotic "time" series (stocks, sunspots, climatological phenomena, DNA patterns, music, serial chemical and physical measurements, humain gait patterns, you name it) is modeled using long- range correlations. Long-range correlated stochastic processes have auto-correlation functions which are not summable (resulting in a pole at DC in the PSD). The long ago past influences the far future. "long range correlation" seems to be a good starting point at Google. Regards, Andor

Posted by ●April 25, 2007

In previous threads, it was mentioned that noise with a Gaussian distribution could be quickly approximated by summing 12 uniform RNG's. Is there an low overhead algorithm to generate samples whose distribution approximates a fat-tailed, extreme kurtosis, Pareto, or power-law decay distributions? This would seem to be useful when simulating or testing filters against noise sources thought to be more turbulent or chaotic than uniform or Gaussian. Thanks, rhn A.T nicholson d.0.t C-o-M