stats::finiteRandom

Generate a random generator for elements of a finite sample space

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

stats::finiteRandom([x1, x2, …], [p1, p2, …], <Seed = n>)
stats::finiteRandom([[x1, p1], [x2, p2], …], <Seed = n>)
stats::finiteRandom(n, <c1, c2>, <Seed = n>)
stats::finiteRandom(n, <[c1, c2]>, <Seed = n>)

Description

stats::finiteRandom([x1, x2, …, xn], [p1, p2, …, pn]) returns a procedure that picks out random elements from the data x1, x2 etc. The chances of picking out elements are given by the probabilities p1, p2 etc.

The procedure f := stats::finiteRandom([x1, x2, …], [p1, p2, …]) can be called in the form f(). The call f() returns one of the data elements x1, x2, ….

The values X = f() are distributed randomly according to the discrete distribution function of the sample space, i.e., the probability of Xx is given by stats::finiteCDF([x1, x2, …], [p1, p2, …])(x).

All probability values p1, p2, … must be convertible to floating-point numbers. They must add up to 1.

Without the option Seed = n, 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::finiteRandom do not react to the environment variable SEED.

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

f := stats::finiteRandom([x1, x2, …], [p1, p2, …]):

f() $k = 1..K;

rather than by

stats::finiteRandom([x_1, x_2, dots], [p_1, p_2, dots])() $k = 1..K;

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

stats::finiteRandom([x_1, x_2, dots], [p_1, p_2, dots], 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.

stats::finiteRandom generalizes stats::empiricalRandom, which assumes equiprobable data. For numerical data x1, x2, …, the call stats::finiteRandom([x_1, dots, x_n], [1/n, dots, 1/n]) corresponds to stats::empiricalRandom([x1, …, xn]).

Examples

Example 1

We pick out random elements of some data:

f := stats::finiteRandom([1, x, y, PI],
                         [1/4, 3/8, 1/4, 1/8],
                                  Seed = 234):
f(), f(), f(), f(), f(), f(), f(), f(), f()

Alternatively, the data may be passed as a list:

f := stats::finiteRandom([[1, 1/4], [x, 3/8],
                          [y, 1/4], [PI, 1/8]],
                                   Seed = 234):
f(), f(), f(), f(), f(), f(), f(), f(), f()

delete f:

Example 2

We create a sample of type stats::sample consisting of one string column and two non-string columns:

s := stats::sample(
  [["1996", 1242, 2/5],
   ["1997", 1353, 0.1],
   ["1998", 1142, 0.2],
   ["1999", 1201, 0.2],
   ["2001", 1201, 0.1]])
"1996"  1242  2/5
"1997"  1353  0.1
"1998"  1142  0.2
"1999"  1201  0.2
"2001"  1201  0.1

We pick random values using the data in the first and third column:

f := stats::finiteRandom(s, 1, 3, Seed = 123):
f(), f(), f(), f(), f(), f(), f()

delete s, f:

Example 3

We toss a loaded coin:

f:= stats::finiteRandom([Head, Tail], [0.4, 0.6], Seed = 123):
f(), f(), f(), f(), f(), f(), f(), f(), f(), f()

We toss the coin 10000 times and count the number of Heads and Tails:

t := [f() $ k = 1..10^4]:
NumberOfHeads = nops(select(t, _equal, Head)),
NumberOfTails = nops(select(t, _equal, Tail))

delete f, t:

Example 4

The probability values must add up to 1:

stats::finiteRandom([Head, TAIL], [0.45, 0.54]):
Error: The probabilities do not add up to one. [stats::finiteRandom]

Parameters

x1, x2, …

The statistical data: arbitrary MuPAD objects

p1, p2, …

Probability values: real numerical values

s

A sample of domain type stats::sample

c1, c2

Column indices of the sample s: positive integers. Column c1 provides the data x1, x2 etc. Column c2 provides the data p1, p2 etc. There is no need to specify column numbers if the sample has only two columns.

Options

Seed

Option, specified as Seed = n

Initializes the random generator with the integer seed n. n 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 values. The generator is initialized with the seed n which may be an arbitrary integer. Several generators with the same initial seed produce the same sequence of values.

Return Values

procedure.

Algorithms

The random values are chosen by applying the quantile function to uniformly distributed random numbers between 0 and 1.

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