NatafInvD: Direct estimation of equivalent correlation coefficients.

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

Description

Direct estimation of equivalent correlation coefficients (i.e., in the Gaussian domain).

Usage

NatafInvD(
  targetrho,
  fx,
  fy,
  paramlistfx,
  paramlistfy,
  NatafIntMethod = "GH",
  NoEval = 19,
  polydeg = 8,
  ...
)

Arguments

targetrho	A scalar or vector of target correlation coefficients.
fx	A string indicating the quantile function of the distribution (i.e., the ICDF).
fy	A string indicating the quantile function of the distribution (i.e., the ICDF).
paramlistfx	A named list with the parameters of the distribution.
paramlistfy	A named list with parameters of the distribution.
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 an alternative parametric curve is fitted (see, Papalexiou, 2018).
...	Additional named arguments for the selected "NatafIntMethod" method.

Value

A named list with two elements: dfnataf: A dataframe that contains the pairs of Gaussian and resulting correlation coefficients, upon which the curve (polynomial or other) was fitted. rzEq: A vector with the equivalent correlation coefficients, that result into the target ones (i.e., targetrho).

Note

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

Examples

## The case of two identrical zero-inflated (i.e., mixed) distributions,
## with p0=0.9 a Gamma distribution
## for the continuous part with shape=0.1 and scale=1.
## Not run: 
fx=fy='qzi'
pfx=pfy=list(Distr=qgamma, p0=0.9, shape=0.1, scale=1)
rhoz=seq(from=0, to=1 , length.out = 21)
rhox=NatafInt(rho = rhoz, fx = fx, fy = fy, paramlistfx = pfx, paramlistfy = pfy)
plot(rhox,rhoz, col='red', pch=19); abline(0,1)
rhotarget=seq(from=0.0001, to=0.9999 , length.out = 210)
req=NatafInvD(targetrho = rhotarget, fx = fx, fy = fy, paramlistfx = pfx, paramlistfy = pfy,
              NatafIntMethod = 'GH', polydeg=8, NoEval = 9)
points(rhotarget, req, col='blue', pch=17);

req=NatafInvD(targetrho = rhotarget, fx = fx, fy = fy, paramlistfx = pfx, paramlistfy = pfy,
              NatafIntMethod = 'GH', polydeg=8, NoEval = 9)
points(rhotarget, req, col='green')

## End(Not run)
## The case with identical Bernoulli distributions, with size=1 and prob=0.2.

## Not run: 
fx=fy='qbinom'
pfx=pfy=list(size=1, prob=0.2)
rhoz=seq(from=0, to=1 , length.out = 21)
rhox=NatafInt(rho = rhoz, fx = fx, fy = fy, paramlistfx = pfx, paramlistfy = pfy)
plot(rhox,rhoz, col='red', pch=19); abline(0,1)
rhotarget=seq(from=0.0001, to=0.9999 , length.out = 210)
req=NatafInvD(targetrho = rhotarget, fx = fx, fy = fy, paramlistfx = pfx, paramlistfy = pfy,
              NatafIntMethod = 'Int', polydeg=8, NoEval = 9)$rzEq
points(rhotarget, req, col='blue', pch=17);

req2=NatafInvD(targetrho = rhotarget, fx = fx, fy = fy, paramlistfx = pfx, paramlistfy = pfy,
              NatafIntMethod = 'Int', polydeg=8, NoEval = 9)$rzEq
points(rhotarget, req2, col='green')

## End(Not run)

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