# inst/Examples/VectIntegral_examples.R In StableEstim: Estimate the Four Parameters of Stable Laws using Different Methods

```## We compute the C matrix as defined in the CGMM paper for length(x)=3
## we challenge the result against the integrate function (compute let by elt)

IntegrateRandomVectorsProduct.example <- function(){
theta <- c(1.5,0.5,1,0)
## Integrands
f_fct <- function(s,x){sapply(X=x,FUN=sampleComplexCFMoment,t=s,theta=theta)}
f_bar_fct <- function(s,x){Conj(f_fct(s,x))}

set.seed(345);X=rstable(3,1.5,0.5,1,0)
## Integration Params
s_min=0;s_max=2
numberIntegrationPoints=100
randomIntegrationLaw="norm"

Estim_Uniform <- IntegrateRandomVectorsProduct(f_fct,X,f_bar_fct,X,s_min,s_max,numberIntegrationPoints,
"Uniform",randomIntegrationLaw)
Estim_Simpson <- IntegrateRandomVectorsProduct(f_fct,X,f_bar_fct,X,s_min,s_max,numberIntegrationPoints,
"Simpson",randomIntegrationLaw)
## Compute the result element by element using integrate
mat <- matrix(0,3,3)
Integrand_real <- function(s,i,j) Re(sampleComplexCFMoment(X[i],s,theta)*Conj(sampleComplexCFMoment(X[j],s,theta))*dnorm(s))
Integrand_Im <- function(s,i,j) Im(sampleComplexCFMoment(X[i],s,theta)*Conj(sampleComplexCFMoment(X[j],s,theta))*dnorm(s))

for (i in 1:3){
for (j in 1:i){
r <-integrate(f=Integrand_real,lower=s_min,upper=s_max,i=i,j=j)\$value
im <- integrate(f=Integrand_Im,lower=s_min,upper=s_max,i=i,j=j)\$value
mat[i,j] <- complex(real=r,imaginary=im)
mat[j,i] <- Conj(mat[i,j])
}
}
list(fct_unif=Estim_Uniform,
fct_Simpson=Estim_Simpson,
integrate=mat)
## User can check the accuracy of the Simpson scheme on this example
}
```

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StableEstim documentation built on May 30, 2017, 12:25 a.m.