Generate a random number generator for Weibull deviates
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Seed = s>)
stats::weibullRandom(a, b) returns a procedure
that produces Weibull deviates
(random numbers) with shape parameter
a > 0 and
b > 0.
f := stats::weibullRandom(a, b) can
be called in the form
f(). The return value of
either a floating-point number or a symbolic expression:
b can be converted
to positive floating-point numbers, then
a nonnegative floating-point number.
In all other cases,
stats::weibullRandom(a, b)() is
Numerical values of
only accepted if they are real and positive.
X = f() are distributed randomly
according to the cumulative distribution function of the Weibull distribution
any 0 ≤ x,
the probability that X ≤ x is
given by .
Without the option
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.
For efficiency, it is recommended to produce sequences of K random numbers via
f := stats::weibullRandom(a, b): f() $k = 1..K;
rather than by
stats::weibullRandom(a, b)() $k = 1..K;
The latter call produces a sequence of generators each of which is called once. Also note that
stats::weibullRandom(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.
The function is sensitive to the environment variable
determines the numerical working precision.
We generate Weibull deviates with parameters
a = 2 and
b = :
f := stats::weibullRandom(2, 3/4): f() $ k = 1..4
With symbolic parameters, no random floating-point numbers can be produced:
f := stats::weibullRandom(a, b): f()
When positive real numbers are assigned to
f starts to produce random floating
a := PI: b := 1/8: f() $ k = 1..4
delete f, a, b:
We use the option
reproduce a sequence of random numbers:
f := stats::weibullRandom(PI, 3, Seed = 1): f() $ k = 1..4
g := stats::weibullRandom(PI, 3, Seed = 1): g() $ k = 1..4
f() = g(), f() = g()
delete f, g:
The shape parameter: an arithmetical expression representing a positive real value
The scale parameter: an arithmetical expression representing a positive real value
Option, specified as
Initializes the random generator with the integer seed
This option serves for generating generators that return predictable
sequences of pseudo-random numbers. The generator is initialized with
When this option is used, the parameters
The implemented algorithm for the computation of the Weibull deviates uses the quantile function of the Weibull distribution applied to unformly distributed random numbers on the interval .