Continuous Distributions
Generic methods for generating independent samples:
- Rejection sampling
- Inverse transform sampling
- Slice sampling
- Ziggurat algorithm, for monotonously decreasing density functions
- Convolution random number generator, not a sampling method in itself: it describes the use of arithmetics on top of one ore more existing sampling methods to generate more involved distributions.
Generic methods for generating correlated samples (often necessary for unusually-shaped or high-dimensional distributions):
- Markov chain Monte Carlo, the general principle
- Metropolis–Hastings algorithm
- Gibbs sampling
- Slice sampling
- Reversible-jump Markov chain Monte Carlo, when the number of dimensions is not fixed (e.g. when estimating a mixture model and simultaneously estimating the number of mixture components)
- Particle filters, when the observed data is connected in a Markov chain and should be processed sequentially
For generating a normal distribution:
- Box–Muller transform
- Marsaglia polar method
For generating a Poisson distribution:
- See Poisson distribution#Generating Poisson-distributed random variables
Read more about this topic: Non-uniform Random Numbers
Famous quotes containing the word continuous:
“For good and evil, man is a free creative spirit. This produces the very queer world we live in, a world in continuous creation and therefore continuous change and insecurity.”
—Joyce Cary (18881957)