Generate a random number generator for uniformly continous deviates
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Seed = s>)
stats::uniformRandom(a, b) returns a procedure
that produces uniformly continous deviates
(random numbers) on the interval .
f := stats::uniformRandom(a, b) can
be called in the form
f(). The return value of
either a floating-point number or a symbolic expression:
b can be converted
to floating-point numbers, then
f() returns a floating
point number between a and b.
In all other cases,
stats::uniformRandom(a, b)() is
Numerical values of
only accepted if they are real and a ≤ b.
X = f() are distributed randomly
according to the cumulative distribution function of the uniform distribution
on the interval .
For any a ≤ x ≤ b,
the probability that X ≤ x is
given by .
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
f := stats::uniformRandom(a, b): f() $ k = 1..K rather
stats::uniformRandom(a, b)() $ k = 1..K The
latter call produces a sequence of generators each of which is called
once. Also note that
stats::uniformRandom(a, b, 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 uniform deviates on the interval :
f := stats::uniformRandom(2, 7): f() $ k = 1..4
With symbolic parameters, no random floating-point numbers can be produced:
f := stats::uniformRandom(a, b): f()
When a and b evaluate
to real numbers,
f starts to produce random floating
a := PI: b := 10: f() $ k = 1..4
delete f, a, b:
We use the option
reproduce a sequence of random numbers:
f := stats::uniformRandom(0, 10, Seed = 10^3): f() $ k = 1..4
g := stats::uniformRandom(0, 10, Seed = 10^3): g() $ k = 1..4
f() = g(), f() = g()
delete f, g:
arithmetical expressions representing real values; a ≤ b is assumed.
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
Uniform deviates on the interval are
a + (b - a)*