Generating Random Variables from Distributions

 

Generating Random Variables from Distributions

General Methods for Continuous Distributions

1. Transformation
   
   : Only suitable for the distribution function F (x) whose inverse F ^ (-1) is not so difficult to evaluate. the first step is to generate U from the uniform distribution; then solve the nonlinear equation F (x)-U = 0 for x. the solution X has the distribution F.
2. Acceptance/Rejection
   
   : Specified ted by von norann in the early days of computing, is one of the most useful general tools in random number generation.
3. Ratio of Uniforms
   
   : The Ratio of Uniforms method is essential a particle form of A/R where the tails of distributions are made more manageable, often leading to short and simple algorithms for each distributions, including discete ones. the key is a simple result by Kinderman and Monahan (1977 ).

General Methods for Discrete Distributions

1. Discrete Inverse
   
2. Acceptance/Rejection
   
3. Ratio of Uniforms
   
4. Walker's Alias Method
   

Reference



1. Numerical Methods of Statistics by John F. Monahan Cambridge University Press; 1st edition (February 15,200 1)
2. http://en.wikipedia.org/wiki/Random_generator


3. Matlab Online Help