| Copyright | (c) 2012 Aleksey Khudyakov |
|---|---|
| License | BSD3 |
| Maintainer | bos@serpentine.com |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell98 |
System.Random.MWC.CondensedTable
Description
Table-driven generation of random variates. This approach can generate random variates in O(1) time for the supported distributions, at a modest cost in initialization time.
- data CondensedTable v a
- type CondensedTableV = CondensedTable Vector
- type CondensedTableU = CondensedTable Vector
- genFromTable :: (PrimMonad m, Vector v a) => CondensedTable v a -> Gen (PrimState m) -> m a
- tableFromProbabilities :: (Vector v (a, Word32), Vector v (a, Double), Vector v a, Vector v Word32) => v (a, Double) -> CondensedTable v a
- tableFromWeights :: (Vector v (a, Word32), Vector v (a, Double), Vector v a, Vector v Word32) => v (a, Double) -> CondensedTable v a
- tableFromIntWeights :: (Vector v (a, Word32), Vector v a, Vector v Word32) => v (a, Word32) -> CondensedTable v a
- tablePoisson :: Double -> CondensedTableU Int
- tableBinomial :: Int -> Double -> CondensedTableU Int
Condensed tables
data CondensedTable v a
A lookup table for arbitrary discrete distributions. It allows
the generation of random variates in O(1). Note that probability
is quantized in units of 1/2^32, and all distributions with
infinite support (e.g. Poisson) should be truncated.
type CondensedTableV = CondensedTable Vector
A CondensedTable that uses boxed vectors, and is able to hold
any type of element.
type CondensedTableU = CondensedTable Vector
A CondensedTable that uses unboxed vectors.
genFromTable :: (PrimMonad m, Vector v a) => CondensedTable v a -> Gen (PrimState m) -> m a
Generate a random value using a condensed table.
Constructors for tables
tableFromProbabilities :: (Vector v (a, Word32), Vector v (a, Double), Vector v a, Vector v Word32) => v (a, Double) -> CondensedTable v a
Generate a condensed lookup table from a list of outcomes with given probabilities. The vector should be non-empty and the probabilites should be non-negative and sum to 1. If this is not the case, this algorithm will construct a table for some distribution that may bear no resemblance to what you intended.
tableFromWeights :: (Vector v (a, Word32), Vector v (a, Double), Vector v a, Vector v Word32) => v (a, Double) -> CondensedTable v a
Same as tableFromProbabilities but treats number as weights not
probilities. Non-positive weights are discarded, and those
remaining are normalized to 1.
tableFromIntWeights :: (Vector v (a, Word32), Vector v a, Vector v Word32) => v (a, Word32) -> CondensedTable v a
Generate a condensed lookup table from integer weights. Weights
should sum to 2^32. If they don't, the algorithm will alter the
weights so that they do. This approach should work reasonably well
for rounding errors.
Disrete distributions
tablePoisson :: Double -> CondensedTableU Int
Create a lookup table for the Poisson distibution. Note that table construction may have significant cost. For λ < 100 it takes as much time to build table as generation of 1000-30000 variates.
Arguments
| :: Int | Number of tries |
| -> Double | Probability of success |
| -> CondensedTableU Int |
Create a lookup table for the binomial distribution.
References
- Wang, J.; Tsang, W. W.; G. Marsaglia (2004), Fast Generation of Discrete Random Variables, /Journal of Statistical Software, American Statistical Association/, vol. 11(i03). http://ideas.repec.org/a/jss/jstsof/11i03.html