# Documentation

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# `stats`::`normalRandom`

Generate a random number generator for normal deviates

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

## Syntax

```stats::normalRandom(`m`, `v`, <`Seed = s`>)
```

## Description

`stats::normalRandom(m, v)` returns a procedure that produces normal deviates (random numbers) with mean m and variance v > 0.

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

If `m` and `v` can be converted to floating-point numbers, `f()` returns a real floating point number. Otherwise, the symbolic call ```stats::normalRandom(m, v)()``` is returned.

Numerical values of `m` and `v` are only accepted if they are real and v is positive.

The values `X = f()` are distributed randomly according to the cumulative distribution function of the normal distribution with parameters `m` and `v`. For any real x, 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::normalRandom` do not react to the environment variable `SEED`.

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.

## Environment Interactions

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

## Examples

### Example 1

We generate normal deviates with mean 2 and variance :

`f := stats::normalRandom(2, 3/4): f() \$ k = 1..4`

`delete f:`

### Example 2

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 point numbers:

`m := PI: v := 1/8: f() \$ k = 1..4`

`delete f, m, v:`

### Example 3

We use the option `Seed` = `s` to 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:`

## Parameters

 `m` The mean: an arithmetical expression representing a real value `v` The variance: an arithmetical expression representing a positive real value

## 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 `m` and `v` must be convertible to suitable floating-point numbers at the time when the random generator is generated.

## Algorithms

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.