graph - How to find probability from a fitted copula in R? -

i need find probability using fitted copula. example, student t copula used. random bivariate variable tsim01 generated rcopula() function on range [0,1].

as understand should compute value of bivariate copula function tcopula @ corresponded points 0< p1, p2<1.

i have tried use function prob() package copula. setup values of p1=0.4, p2=0.7 , small delta=1e-3. have definded small hypercube. probability 0.1036955. example below.

library(copula)  rm(list=ls(all=true)) n <- 100 set.seed(1) df = cbind(as.data.frame(rnorm(n)),             as.data.frame(rnorm(n)));   mymargins      = c("norm", "norm") myparammargins = list(list(mean=mean(df[,1]), sd=sd(df[,1])),                        list(mean=mean(df[,2]), sd=sd(df[,2])))  # student t copula  tcopula  <- tcopula(dim=2, dispstr="un", df=2, df.fixed=true)  tfit     <- fitcopula(tcopula, pobs(as.matrix(df)), method='ml') trho     <- coef(tfit);   tcopula <- mvdc(copula=tcopula(trho, dim=2, df=3),                      margins=mymargins,                      parammargins=myparammargins)               tsim01   <- rcopula(n, tcopula(trho, dim=2, df=3))  p1 <- 0.4; p2 <- 0.7; delta <- 1e-3  prob(tcopula(trho, dim=2, df=3), c(p1, p1+delta), c(p2, p2+delta)) # [1] 0.1036955 

par(mfrow=c(1,3))   persp(tcopula, dmvdc, main="pdf", xlim=c(-2,2), ylim=c(-2,2),          xlab="x", ylab="y", zlab="c(x,y)")   contour(tcopula, dmvdc, main="contour pdf", xlim=c(-2,2), ylim=c(-2,2),           xlab="x", ylab="y")   plot(tsim01, main="tcopula, simulated values on [0,1]^2",         xlab="z1", ylab="z2", pch=16, col="blue")        abline(h=p2,v=p1) 

am correctly applying function prob()? how check answer 3d pdf plot or contour plot?

edit. possible alternative way use a conditional cdf.

edit 2. possible alternative way 2 use quantile transformation c(p1, p2)=t_df_trho(t_df_trho^-1(p1), t_df_trho^-1(p2)).

p1_new <- qt(p1, df=3) # t_df_trho^-1(p1) inverce of t_df_trho() p2_new <- qt(p2, df=3) # t_df_trho^-1(p2) 

but don't know function t_df_trho should use? function t_df_trho bivariate student-t distribution function, df number of degree freedom, , trho correlation coefficient.