EstCorrRVs: Estimation of the auxiliary Gaussian model parameters for the...

In itsoukal/anySim: Stochastic Simulation of Processes with any Marginal Distribution and Correlation Structure

Description

Estimation of the auxiliary Gaussian model parameters for the generation of correlated Random variables (RVs).

Usage

EstCorrRVs(R, dist, params, NatafIntMethod = "GH", NoEval = 9, polydeg = 8)

Arguments

R	A k x k matrix with the target Pearson correlation coefficients among the k RVs.
dist	A k-dimensional string vector indicating the quantile function of the target marginal distributions (i.e., the ICDF) of k RVs.
params	A k-dimensional named list with the parameters of the k target distributions.
NatafIntMethod	A string ("GH", "Int", or "MC") indicating the intergation method to resolve the Nataf integral.
NoEval	A scalar indicating (default: 9) the number of evaluation points for the integration methods.
polydeg	A scalar indicating the order of the fitted polynomial. If polydeg=0, then another curve is fitted.
...	Additional named arguments for the selected "NatafIntMethod" method.

Value

A list with the parameters of the auxiliary Gaussian model.

Note

Avoid the use of the "GH" method (i.e., NatafIntMethod='GH'), when the marginal(s) are discrete.

Examples

## Simulation of 3 correlated RVs with Gamma, Beta and Log-Normal distribution, respectively. 
## We assume also a target correlation matrix.
## Not run: 
set.seed(13)

# Define the target distribution functions (ICDFs) of X1, X2 and X3 RV.
FX1='qgamma'; FX2='qbeta'; FX3='qlnorm'
Distr=c(FX1,FX2,FX3) # store in a vector.

# Define the parameters of the target distribution functions 
# and store them in a list.  
pFX1=list(shape=1.5,scale=2); pFX2=list(shape1=1.5,shape2=3)
pFX3=list(meanlog=1,sdlog=0.5)

DistrParams=list()
DistrParams[[1]]=pFX1;DistrParams[[2]]=pFX2;DistrParams[[3]]=pFX3

# Define the target correlation matrix.
CorrelMat=matrix(c(1,0.7,0.5,
                   0.7,1,0.8,
                   0.5,0.8,1),ncol=3,nrow=3,byrow=T);
            
# Estimate the parameters of the auxiliary Gaussian model.
paramsRVs=EstCorrRVs(R=CorrelMat,dist=Distr,params=DistrParams, 
                        NatafIntMethod='GH',NoEval=9,polydeg=8)

# Generate 10000 synthetic realisations of the 3 correlated RVs.
SynthRVs=SimCorrRVs(n=10000,paramsRVs=paramsRVs)

# Comparison of target and simulation correlation matrix.
pairs(SynthRVs)
CorrelMatSim=cor(SynthRVs)
difference=(CorrelMat-CorrelMatSim)^2; print(difference)

## End(Not run)

itsoukal/anySim documentation built on May 7, 2020, 11:57 p.m.