`.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 R version (for reproducibility).

`set.seed`

is the recommended way to specify seeds.

`.Random.seed <- c(rng.kind, n1, n2, \dots)`

RNGkind(kind = NULL, normal.kind = NULL)
RNGversion(vstr)
set.seed(seed, kind = NULL, normal.kind = NULL)

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`

).

`.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 R version.

`set.seed`

returns `NULL`

, invisibly.

The currently available RNG kinds are given below. `kind`

is
partially matched to this list. The default is
`"Mersenne-Twister"`

.

`"Wichmann-Hill"`

The seed,

`.Random.seed[-1] == r[1:3]`

is an integer vector of length 3, where each`r[i]`

is in`1:(p[i] - 1)`

, where`p`

is the length 3 vector of primes,`p = (30269, 30307, 30323)`

. The Wichmann--Hill generator has a cycle length of \(6.9536 \times 10^{12}\) (=`prod(p-1)/4`

, see*Applied Statistics*(1984)**33**, 123 which corrects the original article).`"Marsaglia-Multicarry"`

:A

*multiply-with-carry*RNG is used, as recommended by George Marsaglia in his post to the mailing list`sci.stat.math`

. It has a period of more than \(2^{60}\) and has passed all tests (according to Marsaglia). The seed is two integers (all values allowed).`"Super-Duper"`

:Marsaglia's famous Super-Duper from the 70's. This is the original version which does

*not*pass the MTUPLE test of the Diehard battery. It has a period of \(\approx 4.6\times 10^{18}\) for most initial seeds. The seed is two integers (all values allowed for the first seed: the second must be odd).We use the implementation by Reeds

*et al*(1982--84).The two seeds are the Tausworthe and congruence long integers, respectively. A one-to-one mapping to S's

`.Random.seed[1:12]`

is possible but we will not publish one, not least as this generator is**not**exactly the same as that in recent versions of S-PLUS.`"Mersenne-Twister"`

:From Matsumoto and Nishimura (1998). A twisted GFSR with period \(2^{19937} - 1\) and equidistribution in 623 consecutive dimensions (over the whole period). The ‘seed’ is a 624-dimensional set of 32-bit integers plus a current position in that set.

`"Knuth-TAOCP-2002"`

:A 32-bit integer GFSR using lagged Fibonacci sequences with subtraction. That is, the recurrence used is $$X_j = (X_{j-100} - X_{j-37}) \bmod 2^{30}% $$ and the ‘seed’ is the set of the 100 last numbers (actually recorded as 101 numbers, the last being a cyclic shift of the buffer). The period is around \(2^{129}\).

`"Knuth-TAOCP"`

:An earlier version from Knuth (1997).

The 2002 version was not backwards compatible with the earlier version: the initialization of the GFSR from the seed was altered. R did not allow you to choose consecutive seeds, the reported ‘weakness’, and already scrambled the seeds.

Initialization of this generator is done in interpreted R code and so takes a short but noticeable time.

`"L'Ecuyer-CMRG"`

:A ‘combined multiple-recursive generator’ from L'Ecuyer (1999), each element of which is a feedback multiplicative generator with three integer elements: thus the seed is a (signed) integer vector of length 6. The period is around \(2^{191}\).

The 6 elements of the seed are internally regarded as 32-bit unsigned integers. Neither the first three nor the last three should be all zero, and they are limited to less than

`4294967087`

and`4294944443`

respectively.This is not particularly interesting of itself, but provides the basis for the multiple streams used in package parallel.

`"user-supplied"`

:Use a user-supplied generator. See

`Random.user`

for details.

`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"`

.

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.
10.1214/aoms/1177706645.

De Matteis, A. and Pagnutti, S. (1993).
Long-range Correlation Analysis of the Wichmann-Hill Random Number
Generator.
*Statistics and Computing*, **3**, 67--70.
10.1007/BF00153065.

Kinderman, A. J. and Ramage, J. G. (1976).
Computer generation of normal random variables.
*Journal of the American Statistical Association*, **71**,
893--896.
10.2307/2286857.

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.
10.1287/opre.47.1.159.

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.
10.1063/1.168514.

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.
10.2307/2347988.

`sample`

for random sampling with and without replacement.

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

```
# NOT RUN {
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
# }
```

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