Generate a random number generator for uniformly continous deviates

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


stats::uniformRandom(a, b, <Seed = s>)


stats::uniformRandom(a, b) returns a procedure that produces uniformly continous deviates (random numbers) on the interval .

The procedure f := stats::uniformRandom(a, b) can be called in the form f(). The return value of f() is either a floating-point number or a symbolic expression:

If a and 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 returned symbolically.

Numerical values of a and b are only accepted if they are real and ab.

The values X = f() are distributed randomly according to the cumulative distribution function of the uniform distribution on the interval . For any axb, the probability that Xx is given by .

Without the option Seed = s, 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.

    Note:   In contrast to the function random, the generators produced by stats::uniformRandom do not react to the environment variable SEED.

For efficiency, it is recommended to produce sequences of K random numbers via f := stats::uniformRandom(a, b): f() $ k = 1..K rather than by 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.

Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision.


Example 1

We generate uniform deviates on the interval :

f := stats::uniformRandom(2, 7): f() $ k = 1..4

delete f:

Example 2

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 point numbers:

a := PI: b := 10: f() $ k = 1..4

delete f, a, b:

Example 3

We use the option Seed = s to 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:


a, b

arithmetical expressions representing real values; ab is assumed.



Option, specified as Seed = s

Initializes the random generator with the integer seed s. s can also be the option CurrentTime, to make the seed depend on the current time.

This option serves for generating generators that return predictable sequences of pseudo-random numbers. The generator is initialized with the seed s which may be an arbitrary integer. Several generators with the same initial seed produce the same sequence of numbers.

When this option is used, the parameters a and b must be convertible to floating-point numbers at the time when the random generator is generated.

Return Values



Uniform deviates on the interval are produced via a + (b - a)*frandom().

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