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I'm facing some precision issues with truncnorm, particularly the ptruncnorm() function in R. Here's an example where I find the cdf up to $q= 2$, where the truncation point is $1.9$, for several truncated normal distributions that differ only in the means of the distribution. 

mean_grid <- seq(-7,0, 0.01)

cdf_list <- c()

for (mean_val in mean_grid) {
  cdf <- ptruncnorm(q = 2, a =1.90, b = Inf, mean = mean_val, sd = 1)
  cdf_list <- c(cdf_list, cdf)
}


plot(x = mean_grid, y = cdf_list, xlab = "truncnorm mean", ylab=  "cdf (X <= 2)")

For mean values (x-axis) at the very left the cdf returns NaN which is reasonable. What I don't understand is that before that, the y-values become haphazard and lose the monotonic pattern in the rest of the graph.

This affects me because I actually want to solve a form: given the truncation point $t$ and a quintile $q$, and an area $c$, solve for a mean $\mu$ such that $\Phi_{t,\mu}(q) = c$, where $\Phi_{t,\mu}$ is the truncated normal cdf. And I use uniroot() to solve this numerically, but if the truncated cdf is not accurate in a region like this then I can't trust the solution.

Does anyone know why this volatility occurs? Am I correct that this is computational precision issue - and if so is there a way to find a more accurate truncated normal cdf?

plots of cdf

woioii
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    Since ptruncnorm is not a standard part of R, please explain what its arguments mean and what it is supposed to return. The code for qnorm.0 I posted at https://stats.stackexchange.com/a/416791/919 shows how to implement the standard Normal quantile function far out into the upper tail--you might find that helpful. It's even easier to implement pnorm far into the tail: see https://stats.stackexchange.com/a/7206/919. Also see the related analysis of truncated Normal means at https://stats.stackexchange.com/a/166277/919. – whuber Sep 19 '19 at 20:57
  • Thank you @whuber. ptruncnorm() is from the truncnorm package, and you identified the crux of the issue: poor definition/behavior in the tails. Looking into this further I saw that the package TruncatedNormal behaves much better in the tails, and it will suffice for my purposes. – woioii Sep 20 '19 at 17:51

0 Answers0