MC1DIntegration
Provides for the integration of a 1-D function via Monte-Carlo sampling.
The evaluation will automatically utilize antithetic sampling to reduce the variance of the estimates unless the user specifies not to do so. In the case of using antithetic sampling, the micro replication sample size refers to the number of independent antithetic pairs observed. Thus, this will require two function evaluations for each micro replication. The user can consider the implication of the cost of function evaluation versus the variance reduction obtained. The default confidence level has been set to 99 percent.
Let f(x) be the probability distribution for the random variable supplied by the sampler. Let g(x) be the function that needs to be integrated. Let h(x) be a factorization of g(x) such that g(x) = h(x)*f(x), that is h(x) = g(x)/f(x)
The interval of integration is defined based on the domain of f(x).
Parameters
the representation of h(x), must not be null
the sampler over the interval, must not be null
true represents use of antithetic sampling
Properties
the desired confidence level
the desired half-width bound for the experiment
the initial sample size for pilot simulation
the maximum number of samples permitted
the number of micro replications to perform
Indicates if initial results are printed
determines whether the reset stream option is on (true) or off (false)
Functions
See page 513 of Law & Kelton
Runs the rth replication for a sequence of replications r = 1, 2, ... , getMicroRepSampleSize()
The purpose of the initial sample is to estimate the variability and determine an approximate number of additional samples needed to meet the desired absolute error. This method must ensure or assumes that no previous sampling has occurred. All statistical accumulators should be reset when this is executed.
Runs numMacroReps macro replications of the micro replications. Does not check half-width or other stopping criteria. Uses the current setting of the number of micro replications per macro replication. Does not perform a pilot run to determine stopping criteria or number of samples to meet desired half-width. Requires 2 or more macro replications.