Generate a random number generator for normal deviates
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Seed = s>)
stats::normalRandom(m, v) returns a procedure
that produces normal deviates
(random numbers) with mean m and
variance v > 0.
f := stats::normalRandom(m, v) can
be called in the form
f(). The return value of
either a floating-point number or a symbolic expression:
v can be converted
to floating-point numbers,
f() returns a real floating
point number. Otherwise, the symbolic call
v)() is returned.
Numerical values of
only accepted if they are real and v is
X = f() are distributed randomly
according to the cumulative distribution function of the normal distribution
any real x,
the probability that X ≤ x is
Without the option
an initial seed is chosen internally. This initial seed is set to
a default value when MuPAD® is started. Thus, each time MuPAD is
started or re-initialized with the
reset function, random generators produce
the same sequences of numbers.
For efficiency, it is recommended to produce sequences of K random numbers via
f := stats::normalRandom(m, v): f() $k = 1..K;
rather than by
stats::normalRandom(m, v)() $k = 1..K;
The latter call produces a sequence of generators each of which is called once. Also note that
stats::normalRandom(m, v, Seed = n)() $k = 1..K;
does not produce a random sequence, because a sequence of freshly initialized generators would be created each of them producing the same number.
The function is sensitive to the environment variable
determines the numerical working precision.
We generate normal deviates with mean 2 and variance :
f := stats::normalRandom(2, 3/4): f() $ k = 1..4
With symbolic parameters, no random floating-point numbers can be produced:
f := stats::normalRandom(m, v): f()
When m and v evaluate
to real numbers,
f starts to produce random floating
m := PI: v := 1/8: f() $ k = 1..4
delete f, m, v:
We use the option
reproduce a sequence of random numbers:
f := stats::normalRandom(PI, 3, Seed = 1): f() $ k = 1..4
g := stats::normalRandom(PI, 3, Seed = 1): g() $ k = 1..4
f() = g(), f() = g()
delete f, g:
The mean: an arithmetical expression representing a real value
The variance: an arithmetical expression representing a positive real value
Option, specified as
Initializes the random generator with the integer seed
This option serves for generating generators that return predictable
sequences of pseudo-random numbers. The generator is initialized with
When this option is used, the parameters
The implemented algorithm for the computation of the normal deviates uses the Box-Mueller method. For more information see: D. Knuth, Seminumerical Algorithms (1998), Vol. 2, pp. 122.