[R] rnorm??

[Adaikalavan Ramasamy]

1) Why do you think there is a bug in rnorm. What is your expected
numbers for cases > 4 or cases < -4 ? If you can show your calculations
then maybe we can see if there is an error in how you calculated it or
with R.


2) Please give a reproducible example. It might be low or high in one
instance on a single run but if you do it several times you may not see
a consistent bias. If you do, then there could be a bug. Otherwise it
could be an element of randomness.

B    <- 10  # increase this if you can 
out1 <- matrix( nr=B, nc=2 )
out2 <- matrix( nr=B, nc=2 )
thr  <- 4

set.seed(1)
for(i in 1:B){
  
  x <- rnorm(1000000)
  out1[ i, 1 ] <- mean( x > thr )    # empirical upper tail prob
  out1[ i, 2 ] <- mean( x < -1*thr ) # empirical lower tail prob

  y <- qnorm(runif(1000000))
  out2[ i, 1 ] <- mean( y > thr )
  out2[ i, 2 ] <- mean( y < -1*thr )

  rm(x, y); print(i)
}

> out1
         [,1]    [,2]
 [1,] 3.6e-05 3.7e-05
 [2,] 3.2e-05 2.6e-05
 [3,] 3.2e-05 2.9e-05
 [4,] 3.7e-05 2.8e-05
 [5,] 3.5e-05 2.5e-05
 [6,] 4.3e-05 3.3e-05
 [7,] 3.9e-05 3.0e-05
 [8,] 3.2e-05 4.8e-05
 [9,] 3.0e-05 3.1e-05
[10,] 3.4e-05 3.7e-05

> out2
         [,1]    [,2]
 [1,] 3.5e-05 2.4e-05
 [2,] 2.4e-05 3.5e-05
 [3,] 4.1e-05 2.6e-05
 [4,] 2.5e-05 3.9e-05
 [5,] 4.1e-05 2.5e-05
 [6,] 4.0e-05 3.1e-05
 [7,] 2.9e-05 2.7e-05
 [8,] 3.1e-05 3.3e-05
 [9,] 3.5e-05 2.5e-05
[10,] 2.7e-05 3.4e-05

The probability of observing any value above 4 or below -4 is pnorm(4,
lower.tail=FALSE) = 3.167124e-05. There does not seem to be anything
suspicious from the run of 10.


3) I think this question might be more appropriate to post this question
to R-devel. Please use an informative subject line. Please read the
posting guide. Thanks.


Regards, Adai



On Mon, 2005-02-21 at 15:45 -0800, Scholz, Fritz wrote:
> I am wondering whether there is a bug in rnorm.
> When generating rnorm(1000000) and counting 
> the cases > 4 and the cases < (-4) I get rather
> unexpectedly low counts for the latter. The problem goes away
> when using qnorm(runif(1000000)).
> 
> Fritz Scholz, PhD
> Applied Statistics Group
> Boeing Phantom Works
> fritz.scholz at pss.boeing.com
> 425-865-3623
> Tu/We 206-542-6545 (most likely)
> 
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