This package regroups and provides a nummber of implementations of the Ziggurat generator for drawing (standard) normally distributed random numbers. Ziggurat was introduced by Marsaglia and Tsang (JSS, 2000) and improved by Leong, Zhang, et al (JSS, 2005).
zrnorm(n)
zrexp(n)
zruni(n)
zrnormLZLLV(n)
zrnormMT(n)
zrnormV1(n)
zrnormVec(x)
zrnormVecV1(x)
zrnormGSL(n)
zrnormQL(n)
zrnormGl(n)
zrnormR(n)
zsetseed(s)
zsetseedV1(s)
zsetseedLZLLV(s)
zsetseedGSL(s)
zsetseedQL(s)
zsetseedGl(s)
zsetseedMT(s)
zgetseed()
zgetseedV1()
zgetpars()
zsetpars(p)The zrnorm* functions all return a vector of the requested
size.
The zsetseed* functions do not return a value, but set the seed
of the generator.
The zgetseed* functions return the (integer) seed. This is
actually not sufficient to capture the state, so zgetpars
zsetpars provide this functionality with a vector of size four.
Use these functions with caution.
Following the original paper, rexp also provides a vector of random
draws from the exponential distribution. In addition, runi offers random
draws from the uniform distribution (which is used internally).
An integer determining the length of the returned N(0,1) (or expoonential or uniform) vector.
A numeric vector, already allocated, that is to filled with N(0,1) draws.
An integer number used to seed the Ziggurat algorithm.
An numeric vector of length four with the state parameters.
Dirk Eddelbuettel
The ‘MT’ variants provide the original Marsaglia and Tsang implementation, updated to work in 32 and 64 bit environments. Their use is not recommended.
The ‘LZLLV’ variants provide the updated Marsaglia and Tsang implementation, based on the comment by Leong, Zhang, Luk, Lee and Villasenor. These versions should be suitable. The code has also been updated to work in 32 and 64 bit environments.
The ‘V1’ variants are based on an earlier implementation by John Burkardt. While fastest, they also correspond to just the Marsaglia and Zhang approach and should not be used.
The function zrnorm() (and corresponding seed setter
zsetseed() and getter zgetseed()) is the recommended
implementation based on merging John Burkardt earlier code with the
Leong et al improvements.
The zrnormGSL functions use the GNU GSL implementation by Jochen Voss.
They too can be recommended for use.
The functions zrnormQL and zrnormGl use, respectively,
functions adapted from the GNU Gretl and QuantLib projects. They have
been added primarily for comparison to the other engines.
The function zrnormR uses the unif_rand uniform
generator from R (which defaults to the Mersenne Twister). It is
useful when the Zigurrat generator is used as a user-supplied
generator in R. However, it stores state in R's internal structures
which makes it a little slower than other alternatives available here.
To turn an N(0,1)-distributed draw into N(mean,sd), multiply by sd and add mean. To turn and Exp(1)-distributed draw into Exp(rate), divide by lambda. Working out how to create a Unif(low, high) from a Unif(0,1) is left as an exercise to the reader. If in doubt, stick with functions from (base) R which are extremely well-tested and widely used.
George Marsaglia and Wai Wan Tsang. The Ziggurat Method for Generating Random Variables. Journal of Statistical Software, Vol 5, Iss 8, Oct 2000 tools:::Rd_expr_doi("10.18637/jss.v005.i08").
Philip H W Leong, Ganglie Zhang, Dong-U Lee, Wayne Luk, and John Villasenor. A Comment on the Implementation of the Ziggurat method, Journal of Statistical Software, Vol 12, Iss 7, Feb 2005 tools:::Rd_expr_doi("10.18637/jss.v012.i07").
Website of John Burkardt. https://people.sc.fsu.edu/~jburkardt/
Website of Jochen Voss. https://www.seehuhn.de/pages/ziggurat
RcppZiggurat-package
set.seed(42)
system.time(replicate(500, rnorm(10000)))
zsetseed(42)
system.time(replicate(500, zrnorm(10000)))
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