R: Convergence problems with numerical integration

问题

Not sure if this numerical methods problem should really be here or in crossvalidated, but since I have a nice reproducible example I though I would start here.

I am going to be estimating and fitting a bunch of distributions both to some large data sets and to data sets generated randomly from similar distributions. As part of this process I will be generating estimates for the conditional mean of various value ranges, including truncated and non-truncated values of the right tail.

The function cr_moment below, given a pdf function for dfun and parameters for that function in params calculates the unconditional mean of that distribution. Given the upper, lower, or both bounds, it calculates the conditional mean for the range specified by those bounds, using the singly- or doubly-truncated distribution for those bounds. The function beneath it, cr_gb2, specializes cr_moment to the generalized beta distribution of the second kind. Finally, the parameter values supplied beneath that approximate the unadjusted current-dollar household income distribution from the US Census/BLS Current Population Survey for the year 2000. McDonald & Ransom 2008. (Also, kudos to Mikko Marttila on this list for help with coding this function).

This function gives me a failure to converge error, copied below, for various lower bounds and an upper bound equal to 4.55e8, or higher, but not at 4.54e8. The kth moment of the GB2 exists for k < shape1 * shape3, here about 2.51. This is a nice smooth unimodal function being integrated over a finite interval, and I don’t know why it is failing to converge and don-t know what to do about it. For other parameter values, but not this one, I have also seen convergence problems at the low end for lower bounds ranging from 6 to a couple of hundred.

Error in integrate(f = prob_interval, lower = lb, upper = ub, subdivisions = 100L):
   the integral is probably divergent

455 billion will be above the highest observable income level, by one or two orders of magnitude, but given a wider range of parameter values and using hill-climbing algorithms to fit real and simulated data I think I will hit this wall many times. I know very little about numerical methods in a case like this and don’t really know where to start. Help and suggestions greatly appreciated.

cr_moment <- function(lb = -Inf, ub = Inf, dfun, params, v=1, ...){
  x_pdf         <- function(X){
    X^v * do.call(what=dfun, args=c(list(x=X), params))
    }
  prob_interval <- function(X){
    do.call(what=dfun, args=c(list(x=X), params))
    }
  integral_val  <- integrate(f = x_pdf, lower = lb, upper = ub)
  integral_prob <- integrate(f = prob_interval, lower = lb, upper = ub)
  crm <-  interval_val[[1]] / interval_prob[[1]]
  out <- list(value = integral_val[[1]], probability = integral_prob[[1]],  
              cond_moment = crm)
  out
}

library(GB2)
cr_gb2 <- function(lb = -Inf, ub = Inf, v = 1, params){
  cr_moment(lb, ub, dfun = dgb2, params = get("params"))
}

GB2_params <- list(shape1 = 2.2474, scale = 58441.5, shape2 = 0.6186, shape3 = 1.118)

cr_gb2(lb=1, ub= 4.55e8, params = GB2_params)

来源：https://stackoverflow.com/questions/49267737/r-convergence-problems-with-numerical-integration