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