# [Rd] Calculation of e^{z^2/2} for a normal deviate z

Rui Barradas ru|pb@rr@d@@ @end|ng |rom @@po@pt
Fri Jun 21 17:30:17 CEST 2019

```Hello,

Sorry, my mistake, I grossly misunderstood the question.

qnorm(1e-300)
#[1] -37.0471

Anyway, you cannot go much smaller.

p <- 10^seq(-300, -400, by = -10)
z <- qnorm(p/2)
exp(z*z/2)

Hope this helps,

Às 16:11 de 21/06/19, jing hua zhao escreveu:
> Dear Rui,
>
> Thanks for your quick reply -- this allows me to see the bottom of this.
> I was hoping we could have a handle of those p in genmoics such as
> 1e-300 or smaller.
>
> Best wishes,
>
>
> Jing Hua
>
> ------------------------------------------------------------------------
> *Sent:* 21 June 2019 15:03
> *To:* jing hua zhao; r-devel using r-project.org
> *Subject:* Re: [Rd] Calculation of e^{z^2/2} for a normal deviate z
> Hello,
>
> Well, try it:
>
> p <- .Machine\$double.eps^seq(0.5, 1, by = 0.05)
> z <- qnorm(p/2)
>
> pnorm(z)
> # [1] 7.450581e-09 1.228888e-09 2.026908e-10 3.343152e-11 5.514145e-12
> # [6] 9.094947e-13 1.500107e-13 2.474254e-14 4.080996e-15 6.731134e-16
> #[11] 1.110223e-16
> p/2
> # [1] 7.450581e-09 1.228888e-09 2.026908e-10 3.343152e-11 5.514145e-12
> # [6] 9.094947e-13 1.500107e-13 2.474254e-14 4.080996e-15 6.731134e-16
> #[11] 1.110223e-16
>
> exp(z*z/2)
> # [1] 9.184907e+06 5.301421e+07 3.073154e+08 1.787931e+09 1.043417e+10
> # [6] 6.105491e+10 3.580873e+11 2.104460e+12 1.239008e+13 7.306423e+13
> #[11] 4.314798e+14
>
>
> p is the smallest possible such that 1 + p != 1 and I couldn't find
>
>
> R version 3.6.0 (2019-04-26)
> Platform: x86_64-pc-linux-gnu (64-bit)
> Running under: Ubuntu 19.04
>
> Matrix products: default
> BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.8.0
> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.8.0
>
> locale:
>    [1] LC_CTYPE=pt_PT.UTF-8       LC_NUMERIC=C
>    [3] LC_TIME=pt_PT.UTF-8        LC_COLLATE=pt_PT.UTF-8
>    [5] LC_MONETARY=pt_PT.UTF-8    LC_MESSAGES=pt_PT.UTF-8
>    [7] LC_PAPER=pt_PT.UTF-8       LC_NAME=C
> [11] LC_MEASUREMENT=pt_PT.UTF-8 LC_IDENTIFICATION=C
>
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods
> [7] base
>
> other attached packages:
>
>
>
> Hope this helps,
>
>
> Às 15:24 de 21/06/19, jing hua zhao escreveu:
>> Dear R-developers,
>>
>> I am keen to calculate exp(z*z/2) with z=qnorm(p/2) and p is very small. I wonder if anyone has experience with this?
>>
>> Thanks very much in advance,
>>
>>
>> Jing Hua
>>
>>        [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-devel using r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>

```