help mata MCatnode()
help mata MCatwt()
help mata tlMCatnode()
help mata tlMCatwt()
help mata intres()
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Title

    Functions for Monte Carlo integration with stratified antithetic sampling
    with rpnfcn()


Syntax

                Command name      Argument

                &MCatnode()       &ab

                &MCatwt()         &ab

                &tlMCatnode()     &a

                &tlMCatwt()       NULL

                &intres()         NULL


Description

    These functions are to be used with rpnfcn(). The functions &MCatnode(),
    &MCatwt(), &tlMCatnode(), and &tlMCatwt() compute nodes and weights for
    numerical integration based on Monte Carlo with stratified antithetic
    sampling. The function &intres() computes the result by summing the
    evaluated nodes multiplied with the weights.

Remarks

    &MCatnode() and &tlMCatnode() use the argument vector ab and a,
    respectively, to set up the nodes based on the matrix of uniformly
    distributed random variables presumed to be in the current top element of
    the stack in rpnfcn(). The number of columns of the matrix of uniformly
    distributed random variables equals the number of strata used in the
    integration, thus precision is improved when the number of columns is
    increased. ab must be a matrix with two columns specifying the lower and
    upper boundary of the integration interval, respectively, while a must be
    a column vector specifying the lower boundary for the indefinite
    integral.



Source code

    rpnint.mata

Author

    Henrik Støvring, Research Unit of General Practice, University of
    Southern Denmark.  Please email hstovring@health.sdu.dk if you have
    comments, questions or observe any problems.


Also see

    Manual:  [M] Mata Reference Manual

    Online:  help for [M-0] mata,  Evaluation of algorithm matrix using RPN,
             RPN stack manipulation functions, RPN binary operators, RPN
             distribution functions,