#' returns approximate sample from truncated invarse gamma distribution
#' @param lis: a list containing lis$alpha, lis$beta, lis$l = lower bound , lis$u = upper bound 
#' 
rTIgammaInvCdf<-function(lis){
  #print("inside rTIgammaInvCdf")
  alpha=lis$alpha
  beta=lis$beta
  Lower=lis$l
  Upper=lis$u
  G0 <- Gammad(scale =(1/beta), shape = alpha) ## generates a Gamma distribution 
  G <- 1/G0 ## the corresponding inverse Gamma
  TG <- Truncate(G, lower=Lower, upper=Upper) 
  return( ( q(TG)(runif(1,0,1)))  )
}