simEd (version 2.0.0)

vexp: Variate Generation for Exponential Distribution

Description

Variate Generation for Exponential Distribution

Usage

vexp(n, rate = 1, stream = NULL, antithetic = FALSE, asList = FALSE)

Arguments

n

number of observations

rate

Rate of distribution (default 1)

stream

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

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

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 exponential random variates

quantile

Parameterized quantile function

text

Parameterized title of distribution

Details

Generates random variates from the exponential distribution.

Exponential 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::qexp is used to invert the uniform(0,1) variate(s). In this way, using vexp 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 exponential distribution with rate \(\lambda\) has density

$$f(x) = \lambda e^{-\lambda x}$$

for \(x \geq 0\).

See Also

rstream, set.seed, stats::runif

stats::rexp

Examples

# NOT RUN {
 set.seed(8675309)
 # NOTE: following inverts rstream::rstream.sample using stats::qexp
 vexp(3, rate = 2)

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

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

 set.seed(8675309)
 variates <- vexp(1000, 2, stream = 1)
 set.seed(8675309)
 variates <- vexp(1000, 2, stream = 1, antithetic = TRUE)

 set.seed(8675309)
 # NOTE: Default functions for M/M/1 ssq(), ignoring fixed n
 interarrivals <- vexp(1000, rate = 1,    stream = 1)
 services      <- vexp(1000, rate = 10/9, stream = 2)

# }