Acceptance-Rejection Algorithm Visualization
This function animates the process of generating variates via acceptance-rejection for a specified density function (pdf) bounded by a specified majorizing function.
accrej( n = 20, pdf = function(x) dbeta(x, 3, 2), majorizingFcn = NULL, majorizingFcnType = NULL, support = c(0, 1), seed = NA, maxTrials = Inf, plot = TRUE, showTitle = TRUE, plotDelay = plot * -1 )
n |
number of variates to generate. |
pdf |
desired probability density function from which random variates are to be drawn |
majorizingFcn |
majorizing function. Default value is NULL, corresponding to a constant majorizing function that is 1.01 times the maximum value of the pdf. May alternatively be provided as a user-specified function, or as a data frame requiring additional notation as either piecewise-constant or piecewise-linear. See examples. |
majorizingFcnType |
used to indicate whether a majorizing function that
is provided via data frame is to be interpreted as
either piecewise-constant ( |
support |
the lower and upper bounds of the support of the probability distribution of interest, specified as a two-element vector. |
seed |
initial seed for the uniform variates used during generation. |
maxTrials |
maximum number of accept-reject trials; infinite by default |
plot |
if TRUE, visual display will be produced. If FALSE, generated variates will be returned without visual display. |
showTitle |
if TRUE, display title in the main plot. |
plotDelay |
wait time, in seconds, between plots; -1 (default) for interactive mode, where the user is queried for input to progress. |
There are three modes for visualizing the acceptance-rejection algorithm for generating random variates from a particular probability distribution:
interactive advance (plotDelay = -1), where
pressing the 'ENTER' key advances to the next step
(an accepted random variate) in the algorithm,
typing 'j #' jumps ahead # steps,
typing 'q' quits immediately,
and typing 'e' proceeds to the end;
automatic advance (plotDelay > 0); or
final visualization only (plotDelay = 0).
As an alternative to visualizing, variates can be generated
Returns the n generated variates accepted.
accrej(n = 20, seed = 8675309, plotDelay = 0)
## Not run:
accrej(n = 10, seed = 8675309, plotDelay = 0.1)
accrej(n = 10, seed = 8675309, plotDelay = -1)
# Piecewise-constant majorizing function
m <- function(x) {
if (x < 0.3) 1.0
else if (x < 0.85) 2.5
else 1.5
}
accrej(n = 100, seed = 8675309, majorizingFcn = m, plotDelay = 0)
# Piecewise-constant majorizing function as data frame
m <- data.frame(
x = c(0.0, 0.3, 0.85, 1.0),
y = c(1.0, 1.0, 2.5, 1.5))
accrej(n = 100, seed = 8675309, majorizingFcn = m,
majorizingFcnType = "pwc", plotDelay = 0)
# Piecewise-linear majorizing function as data frame
m <- data.frame(
x = c(0.0, 0.1, 0.3, 0.5, 0.7, 1.0),
y = c(0.0, 0.5, 1.1, 2.2, 1.9, 1.0))
accrej(n = 100, seed = 8675309, majorizingFcn = m,
majorizingFcnType = "pwl", plotDelay = 0)
# invalid majorizing function; should give warning
accrej(n = 20, majorizingFcn = function(x) dbeta(x, 1, 3), plotDelay = 0)
## End(Not run)
# Piecewise-linear majorizing function with power-distribution density function
m <- data.frame(x = c(0, 1, 2), y = c(0, 0.375, 1.5))
samples <- accrej(n = 100, pdf = function(x) (3 / 8) * x ^ 2, support = c(0,2),
majorizingFcn = m, majorizingFcnType = "pwl", plotDelay = 0)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.