simEd (version 2.0.1)

vweibull: Variate Generation for Weibull Distribution

Description

Variate Generation for Weibull Distribution

Usage

vweibull(
  n,
  shape,
  scale = 1,
  stream = NULL,
  antithetic = FALSE,
  asList = FALSE
)

Value

If asList is FALSE (default), return a vector of random variates.

Otherwise, return a list with components suitable for visualizing inversion, specifically:

u

A vector of generated U(0,1) variates

x

A vector of Weibull random variates

quantile

Parameterized quantile function

text

Parameterized title of distribution

Arguments

n

number of observations

shape

Shape parameter

scale

Scale parameter (default 1)

stream

if NULL (default), uses stats::runif to generate uniform variates to invert via stats::qweibull; otherwise, an integer in 1:25 indicates the rstream stream from which to generate uniform variates to invert via stats::qweibull;

antithetic

if FALSE (default), inverts \(u\) = uniform(0,1) variate(s) generated via either stats::runif or rstream::rstream.sample; otherwise, uses \(1 - u\)

asList

if FALSE (default), output only the generated random variates; otherwise, return a list with components suitable for visualizing inversion. See return for details

Author

Barry Lawson (),
Larry Leemis (),
Vadim Kudlay ()

Details

Generates random variates from the Weibull distribution.

Weibull variates are generated by inverting uniform(0,1) variates produced either by stats::runif (if stream is NULL) or by rstream::rstream.sample (if stream is not NULL). In either case, stats::qweibull is used to invert the uniform(0,1) variate(s). In this way, using vweibull provides a monotone and synchronized binomial variate generator, although not particularly fast.

The stream indicated must be an integer between 1 and 25 inclusive.

The Weibull distribution with parameters shape = \(a\) and scale = \(b\) has density

 \deqn{f(x) = \frac{a}{b} \left(\frac{x}{b}\right)^{a-1} e^{-(x/b)^a}}{
           f(x) = (a/b) (x/b)^(a-1) exp(-(x/b)^a)}

for \(x \ge 0\), \(a > 0\), and \(b > 0\).

See Also

rstream, set.seed, stats::runif

stats::rweibull

Examples

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qweibull
 vweibull(3, shape = 2, scale = 1)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qweibull
 vweibull(3, 2, 1, stream = 1)
 vweibull(3, 2, 1, stream = 2)

 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qweibull
 vweibull(1, 2, 1, stream = 1)
 vweibull(1, 2, 1, stream = 2)
 vweibull(1, 2, 1, stream = 1)
 vweibull(1, 2, 1, stream = 2)
 vweibull(1, 2, 1, stream = 1)
 vweibull(1, 2, 1, stream = 2)

 set.seed(8675309)
 variates <- vweibull(100, 2, 1, stream = 1)
 set.seed(8675309)
 variates <- vweibull(100, 2, 1, stream = 1, antithetic = TRUE)