# stats::uniformRandom

Generate a random number generator for uniformly continous deviates

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

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

## Description

`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.

## Examples

### 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:`

## Parameters

 `a`, `b` arithmetical expressions representing real values; a ≤ b is assumed.

## Options

 `Seed` 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.

## Algorithms

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