EstSPARTA: Estimation of the auxiliary PAR(1) model parameters

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

Description

Estimation of parameters of the auxiliary PAR(1) model to simulate the auxiliary cyclostationary Gaussian process to establish the target season-to-season correlation structure.

Usage

EstSPARTA(
  s2srtarget,
  dist,
  params,
  NatafIntMethod = "GH",
  NoEval = 9,
  polydeg = 6,
  ...
)

Arguments

s2srtarget	A k-dimensional vector with the lag-1 season-to-season correlation coefficients.
dist	A k-dimensional string vector indicating the quantile function of the target marginal distributions (i.e., the ICDFs).
params	A k-dimensional named list with the parameters of the target distributions.
NatafIntMethod	A string ("GH", "Int", or "MC") indicating the integration 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 cyclostationary auxiliary Gaussian PAR(1) model.

Note

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

Examples

## Simulation of univariate cyclostationary process with specific distribution function at each season 
## and specific lag-1 season-to-season correlations.
## Not run: 
set.seed(21)

# Define the number of seasons.
NumOfSeasons=12 # number of months 

# Define the lag-1 season-to-season correlation coefficients (12 values).
rtarget<-c(0.05,0.55,0.45,0.4,0.6,0.75,0.7,0.75,0.5,0.3,0.3,0.2)

# Define the target distribution functions for each season.
# In this example, a re-parameterized version of Gen. Gamma distribution is used.
qgengamma=function(p,scale, shape1, shape2){
  require(VGAM)
  X=qgengamma.stacy(p=p,scale=scale,k=(shape1/shape2),d=shape2)
  return(X)
}

# Or, a re-parameterized version of Burr Type XII distribution.
qburr=function(p,scale,shape1,shape2) {
  require(ExtDist)
  x=ExtDist::qBurr(p=p,b=scale,g=shape1,s=shape2)
  return(x)
}

# Here, we define the target distribution of each season, though being of continuous type,
# as a zero-inflated ones to demonstrate the more general case. Alternatively, the definition
# could be conducted as in the example of EstARTAp function.

FXs<-rep('qmixed',NumOfSeasons) # Define that distributions are of zero-inflated type.

# Define the parameters of the zero-inflated distribution function for each season.
PFXs<-vector("list",NumOfSeasons)
PFXs[[1]]=list(p0=0.0,Distr=qgengamma,scale=47.22,shape1=2.7,shape2=0.97)
PFXs[[2]]=list(p0=0.0,Distr=qgengamma,scale=199.4,shape1=1.74,shape2=3.45)
PFXs[[3]]=list(p0=0.0,Distr=qburr,scale=193.2,shape1=3.07,shape2=2.54)
PFXs[[4]]=list(p0=0.0,Distr=qburr,scale=172.16,shape1=4.42,shape2=2.50)
PFXs[[5]]=list(p0=0.0,Distr=qgengamma,scale=53.40,shape1=4.11,shape2=1.66)
PFXs[[6]]=list(p0=0.0,Distr=qgengamma,scale=0.017,shape1=26.23,shape2=0.51)
PFXs[[7]]=list(p0=0.0,Distr=qgengamma,scale=27.70,shape1=5.15,shape2=5.30)
PFXs[[8]]=list(p0=0.0,Distr=qgengamma,scale=0.33,shape1=30.97,shape2=0.876)
PFXs[[9]]=list(p0=0.0,Distr=qburr,scale=14.46,shape1=7.6,shape2=0.44)
PFXs[[10]]=list(p0=0.0,Distr=qburr,scale=29.36,shape1=2.73,shape2=0.87)
PFXs[[11]]=list(p0=0.0,Distr=qgengamma,scale=53.15,shape1=3.12,shape2=1.4)
PFXs[[12]]=list(p0=0.0,Distr=qgengamma,scale=116.02,shape1=2.21,shape2=1.33)

# Estimate the parameters of SPARTA model.
SPARTApar<-EstSPARTA(s2srtarget=rtarget,dist=FXs,params=PFXs,
            NatafIntMethod='GH',NoEval=9,polydeg=8,nodes=11)
            
# Generate a synthetic series of 10000 length.
simSPARTA<-SimSPARTA(SPARTApar=SPARTApar,steps=10^5)

## End(Not run)

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