Accelerating the pace of engineering and science

# Documentation Center

• Trial Software

# stats::geometricRandom

Generate a random number generator for geometric deviates

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::geometricRandom(p, <Seed = s>)
```

## Description

stats::geometricRandom(p) returns a procedure that produces geometric deviates (random numbers) with `probability parameter' p.

The procedure f:=stats::geometricRandom(p) can be called in the form f(). The return value of f() is a positive integer if p is a real number satisfying 0 ≤ p ≤ 1.

Otherwise, stats::geometricRandom(p)() is returned symbolically.

Numerical values for p are only accepted if they satisfy 0 ≤ p ≤ 1.

The values X = f() are distributed randomly according to the discrete distribution function of the geometric distribution with parameter p, i.e., for 1 ≤ x, the probability of 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:   With this option, the parameter p must evaluate to a numerical value at the time, when the generator is created.
 Note:   In contrast to the function random, the generators produced by stats::geometricRandom do not react to the environment variable SEED.

For efficiency, it is recommended to produce sequences of K random numbers via

f := stats::geometricRandom(p): f() \$k = 1..K;

rather than by

stats::geometricRandom(p)() \$k = 1..K;

The latter call produces a sequence of generators each of which is called once. Also note that

stats::geometricRandom(p, Seed = s)() \$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 geometric deviates with :

`f := stats::geometricRandom(1/3): f() \$ k = 1..10`

`delete f:`

### Example 2

With symbolic parameters, no random floating-point numbers can be produced:

`f := stats::geometricRandom(p): f()`

When p evaluates to a real number between 0 and 1, the generator starts to produce random numbers:

`p := 1/sqrt(70): f(), f(), f()`

`delete f, p:`

### Example 3

We use the option Seed = s to reproduce a sequence of random numbers:

`f := stats::geometricRandom(1/10, Seed = 1): f() \$ k = 1..10`

`g := stats::geometricRandom(1/10, Seed = 1): g() \$ k = 1..10`

`f() = g(), f() = g()`

`delete f, g:`

## Parameters

 p The "probability parameter": an arithmetical expression representing a real number 0 ≤ p ≤ 1.

## 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 parameter p must be convertible to a floating-point number between 0.0 and 1.0 at the time when the random generator is generated.