Case Studies

Dim=2, equal marginals

for(i in seq_along(cases)) {
   if(!endsWith(cases[i], "D2")) next
   tmp=case.studies(i, 2000)
   print(cases[i])
   p=tmp$param_alt[2]
   if(startsWith(cases[i],"Dalitz")) p=10*p
   dta=tmp$f(p)
   dtax=data.frame(x=dta$x[,1], y=dta$x[,2])
   dtay=data.frame(x=dta$y[,1], y=dta$y[,2])
   px=ggplot2::ggplot(dtax, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="blue", alpha=0.5, size=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
     
   py=ggplot2::ggplot(dtay, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="red", alpha=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
  multiple.graphs(px, py, cases[i])
}
#> [1] "NormalD2"

#> [1] "tD2"

#> [1] "UniformMixtureD2"

#> [1] "FrankD2"

#> [1] "ClaytonD2"

#> [1] "GumbelD2"

#> [1] "GalambosD2"

#> [1] "HuslerReissD2"

#> [1] "ClaytonGumbelD2"

#> [1] "UniformFrankD2"

#> [1] "ParetoSimplexD2"

#> [1] "KhoudrajiClaytonD2"

#> [1] "NormalUniformD2"

#> [1] "JoeD2"

#> [1] "DalitzCleoD2"

#> [1] "DalitzPDGD2"

#> [1] "DalitzBabarD2"

Dim=2, unequal marginals

for(i in seq_along(cases)) {
   if(!endsWith(cases[i], "M")) next
   tmp=case.studies(i, 2000)
   print(cases[i])
   p=tmp$param_alt[2]
   if(startsWith(cases[i],"Dalitz")) p=10*p
   dta=tmp$f(p)
   dtax=data.frame(x=dta$x[,1], y=dta$x[,2])
   dtay=data.frame(x=dta$y[,1], y=dta$y[,2])
   px=ggplot2::ggplot(dtax, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="blue", alpha=0.5, size=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
     
   py=ggplot2::ggplot(dtay, ggplot2::aes(x=x, y=y))+
     ggplot2::geom_point(color="red", alpha=0.5)+
     ggplot2::labs(x=expression(x[1]), y=expression(x[2])) 
  multiple.graphs(px, py, cases[i])
}
#> [1] "NormalShiftM"

#> [1] "NormalStretchM"

#> [1] "UniformRotateM"

#> [1] "UniformBetaM"

#> [1] "TruncExponentialM"

#> [1] "DalitzCleoM"

#> [1] "DalitzPDGM"

#> [1] "DalitzBabarM"

#> [1] "FrankExponentialM"

#> [1] "FrankLinearM"

#> [1] "FrankNormalM"

#> [1] "ClaytonExponentialM"

#> [1] "ClaytonLinearM"

#> [1] "ClaytonNormalM"

#> [1] "GalambosExponentialM"

#> [1] "GalambosLinearM"

#> [1] "GalambosNormalM"

Dim=5, equal marginals

• NormalD5: multivariate normal distribution with equal marginals.
  
• tD5: multivariate t distribution with 5 degrees of freedom and equal marginals.
  
• FrankD5: Frank cupola.
  
• ClaytonD5: Clayton cupola.
  
• GumbelD5: Gumbel copula.
  
• JoeD5: Joe cupola.
  
• UniformFrankD5: mixture of uniform and Frank cupola.
  
• FrankClaytonD5: mixture of Frank and Clayton cupolas.
  
• FrankJoeD5: mixture of Frank and Joe cupolas.

Dim=5, unequal marginals

• UniformExponentialM5: Exponential distributions.
  
• FrankExponentialM5: Frank cupola with exponential marginals.
  
• FrankLinearM5: Frank cupola with linear marginals.
  
• FrankNormalM5: Frank cupola with linear marginals.
  
• ClaytonExponentialM5: Clayton cupola with exponential marginals.
  
• ClaytonLinearM5: Clayton cupola with linear marginals.
  
• ClaytonNormalM5: Clayton cupola with linear marginals.