|Copyright||(c) 2012 Aleksey Khudyakov|
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
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.
CondensedTable that uses boxed vectors, and is able to hold
any type of element.
Generate a random value using a condensed table.
Constructors for tables
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.
tableFromProbabilities but treats number as weights not
probilities. Non-positive weights are discarded, and those
remaining are normalized to 1.
Generate a condensed lookup table from integer weights. Weights
should sum to
2^32 at least approximately. This function will
correct small deviations from
2^32 such as arising from rounding
errors. But for large deviations it's likely to product incorrect
result with terrible performance.
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.
Create a lookup table for the binomial distribution.
- 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