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Encyclopedia > Ziggurat algorithm

The ziggurat algorithm generates normally-distributed random variables. It was developed by George Marsaglia. The algorithm is considerably faster than the two more commonly used methods, the Marsaglia polar method or the Box-Muller transform, because the former requires a logarithm, a square root and rejects random points in a square that do not fall in the inscribed circle, while the latter requires a logarithm, square root, sine and cosine. The ziggurat algorithm on the other hand can generate normally-distributed random variables nearly as fast as uniformly-distributed ones. The normal distribution, also called Gaussian distribution by scientists (named after Carl Friedrich Gauss due to his rigorous application of the distribution to astronomical data (Havil, 2003)), is a continuous probability distribution of great importance in many fields. ... A random variable is a mathematical function that maps outcomes of random experiments to numbers. ... George Marsaglia is a professor of statistics at Florida State University. ... The Marsaglia polar method is a widely used method for generating a pair of independent standard normal random variables by choosing random points in the square until , then returning the required pair of normal random variables as . The underlying theory may be summarized as follows: If is uniformly distributed in... Diagram of the Box Muller transform. ... In mathematics, the uniform distributions are simple probability distributions. ...


The ziggurat algorithm can also be used to generate random variabless for the exponential distribution and other decreasing density distributions. A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ... In probability theory and statistics, the exponential distributions are a class of continuous probability distribution. ...


The ziggurat algorithm is named after ziggurats because the basis of the algorithm is a step function which resembles a ziggurat. Dur-Untash, or Choqa Zanbil, built in 13th century BC by Untash Napirisha and located near Susa, Iran is one of the worlds best-preserved ziggurats. ...


See also

Diagram of the Box Muller transform. ... A random number generator is a computational or physical device designed to generate a sequence of elements (usually numbers), such that the sequence can be used as a random one. ...

References

  • Ziggurat algorithm generates normally distributed random numbers
  • The Ziggurat Method for Generating Random Variables
  • C implementation of the ziggurat method for the normal density function and the exponential density function

 
 

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