# Random

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##### Random Number Generation

.Random.seed is an integer vector, containing the random number generator (RNG) state for random number generation in R. It can be saved and restored, but should not be altered by the user.

RNGkind is a more friendly interface to query or set the kind of RNG in use.

RNGversion can be used to set the random generators as they were in an earlier Rversion (for reproducibility).

set.seed is the recommended way to specify seeds.

Keywords
distribution, sysdata
##### Usage
.Random.seed <- c(rng.kind, n1, n2, ...)RNGkind(kind = NULL, normal.kind = NULL)
RNGversion(vstr)
set.seed(seed, kind = NULL, normal.kind = NULL)
##### Arguments
kind
character or NULL. If kind is a character string, set R's RNG to the kind desired. Use "default" to return to the R default. See ‘Details’ for the interpretation of NULL.
normal.kind
character string or NULL. If it is a character string, set the method of Normal generation. Use "default" to return to the R default. NULL makes no change.
seed
a single value, interpreted as an integer, or NULL (see ‘Details’).
vstr
a character string containing a version number, e.g., "1.6.2"
rng.kind
integer code in 0:k for the above kind.
n1, n2, ...
integers. See the details for how many are required (which depends on rng.kind).
##### Details

The currently available RNG kinds are given below. kind is partially matched to this list. The default is "Mersenne-Twister". [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

normal.kind can be "Kinderman-Ramage", "Buggy Kinderman-Ramage" (not for set.seed), "Ahrens-Dieter", "Box-Muller", "Inversion" (the default), or "user-supplied". (For inversion, see the reference in qnorm.) The Kinderman-Ramage generator used in versions prior to 1.7.0 (now called "Buggy") had several approximation errors and should only be used for reproduction of old results. The "Box-Muller" generator is stateful as pairs of normals are generated and returned sequentially. The state is reset whenever it is selected (even if it is the current normal generator) and when kind is changed.

set.seed uses a single integer argument to set as many seeds as are required. It is intended as a simple way to get quite different seeds by specifying small integer arguments, and also as a way to get valid seed sets for the more complicated methods (especially "Mersenne-Twister" and "Knuth-TAOCP"). There is no guarantee that different values of seed will seed the RNG differently, although any exceptions would be extremely rare. If called with seed = NULL it re-initializes (see Note) as if no seed had yet been set.

The use of kind = NULL or normal.kind = NULL in RNGkind or set.seed selects the currently-used generator (including that used in the previous session if the workspace has been restored): if no generator has been used it selects "default".

##### Value

• .Random.seed is an integer vector whose first element codes the kind of RNG and normal generator. The lowest two decimal digits are in 0:(k-1) where k is the number of available RNGs. The hundreds represent the type of normal generator (starting at 0).

In the underlying C, .Random.seed[-1] is unsigned; therefore in R.Random.seed[-1] can be negative, due to the representation of an unsigned integer by a signed integer.

RNGkind returns a two-element character vector of the RNG and normal kinds selected before the call, invisibly if either argument is not NULL. A type starts a session as the default, and is selected either by a call to RNGkind or by setting .Random.seed in the workspace.

RNGversion returns the same information as RNGkind about the defaults in a specific Rversion.

set.seed returns NULL, invisibly.

##### Note

Initially, there is no seed; a new one is created from the current time and the process ID when one is required. Hence different sessions will give different simulation results, by default. However, the seed might be restored from a previous session if a previously saved workspace is restored.

.Random.seed saves the seed set for the uniform random-number generator, at least for the system generators. It does not necessarily save the state of other generators, and in particular does not save the state of the Box--Muller normal generator. If you want to reproduce work later, call set.seed (preferably with explicit values for kind and normal.kind) rather than set .Random.seed.

The object .Random.seed is only looked for in the user's workspace.

Do not rely on randomness of low-order bits from RNGs. Most of the supplied uniform generators return 32-bit integer values that are converted to doubles, so they take at most $2^{32}$ distinct values and long runs will return duplicated values (Wichmann-Hill is the exception, and all give at least 30 varying bits.)

##### References

Ahrens, J. H. and Dieter, U. (1973) Extensions of Forsythe's method for random sampling from the normal distribution. Mathematics of Computation 27, 927-937.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. (set.seed, storing in .Random.seed.)

Box, G. E. P. and Muller, M. E. (1958) A note on the generation of normal random deviates. Annals of Mathematical Statistics 29, 610--611.

De Matteis, A. and Pagnutti, S. (1993) Long-range Correlation Analysis of the Wichmann-Hill Random Number Generator, Statist. Comput., 3, 67--70.

Kinderman, A. J. and Ramage, J. G. (1976) Computer generation of normal random variables. Journal of the American Statistical Association 71, 893-896.

Knuth, D. E. (1997) The Art of Computer Programming. Volume 2, third edition. Source code at http://www-cs-faculty.stanford.edu/~knuth/taocp.html.

Knuth, D. E. (2002) The Art of Computer Programming. Volume 2, third edition, ninth printing.

L'Ecuyer, P. (1999) Good parameters and implementations for combined multiple recursive random number generators. Operations Research 47, 159--164.

Marsaglia, G. (1997) A random number generator for C. Discussion paper, posting on Usenet newsgroup sci.stat.math on September 29, 1997.

Marsaglia, G. and Zaman, A. (1994) Some portable very-long-period random number generators. Computers in Physics, 8, 117--121.

Matsumoto, M. and Nishimura, T. (1998) Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Transactions on Modeling and Computer Simulation, 8, 3--30. Source code formerly at http://www.math.keio.ac.jp/~matumoto/emt.html. Now see http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/C-LANG/c-lang.html. Reeds, J., Hubert, S. and Abrahams, M. (1982--4) C implementation of SuperDuper, University of California at Berkeley. (Personal communication from Jim Reeds to Ross Ihaka.)

Wichmann, B. A. and Hill, I. D. (1982) Algorithm AS 183: An Efficient and Portable Pseudo-random Number Generator, Applied Statistics, 31, 188--190; Remarks: 34, 198 and 35, 89.

sample for random sampling with and without replacement.

Distributions for functions for random-variate generation from standard distributions.

• Random
• RNG
• RNGkind
• RNGversion
• set.seed
• .Random.seed
##### Examples
library(base) require(stats) ## the default random seed is 626 integers, so only print a few runif(1); .Random.seed[1:6]; runif(1); .Random.seed[1:6] ## If there is no seed, a "random" new one is created: rm(.Random.seed); runif(1); .Random.seed[1:6] ok <- RNGkind() RNGkind("Wich") # (partial string matching on 'kind') ## This shows how 'runif(.)' works for Wichmann-Hill, ## using only R functions: p.WH <- c(30269, 30307, 30323) a.WH <- c( 171, 172, 170) next.WHseed <- function(i.seed = .Random.seed[-1]) { (a.WH * i.seed) %% p.WH } my.runif1 <- function(i.seed = .Random.seed) { ns <- next.WHseed(i.seed[-1]); sum(ns / p.WH) %% 1 } rs <- .Random.seed (WHs <- next.WHseed(rs[-1])) u <- runif(1) stopifnot( next.WHseed(rs[-1]) == .Random.seed[-1], all.equal(u, my.runif1(rs)) ) ## ---- .Random.seed RNGkind("Super") # matches "Super-Duper" RNGkind() .Random.seed # new, corresponding to Super-Duper ## Reset: RNGkind(ok[1]) ## ---- sum(duplicated(runif(1e6))) # around 110 for default generator ## and we would expect about almost sure duplicates beyond about qbirthday(1 - 1e-6, classes = 2e9) # 235,000
Documentation reproduced from package base, version 3.3, License: Part of R @VERSION@

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