[R] Solving a normal distribution pnorm for q

[Eik Vettorazzi]

Assuming r, sd1 and sd2 as known(fixed) components, this works:

X <- pnorm(q=q,sd=sd1)*r+pnorm(q=q,sd=sd2)*(1-r)
uniroot(function(x)pnorm(q=x,sd=sd1)*r+pnorm(q=x,sd=sd2)*(1-r)-X,c(-1e6,1e6))


Cheers

Am 12.12.2013 15:58, schrieb Johannes Radinger:
> Thanks for the fast response. Of course I totally overlooked qnorm as I had
> a more complex task in my head.
> 
> I wanted to reverse following equation:
> r=0.67
> q=-150
> sd1=100
> sd2=1000
> 
> X <- pnorm(q=q,sd=sd1)*r+pnorm(q=q,sd=sd2)*(1-r)
> 
> Maybe its mathematically really easy, but somehow I don't get it how to do
> reverse and provide X and
> get q especially with the presence of r respectively as weighting factors
> for the two distributions.
> 
> /J
> 
> 
> On Thu, Dec 12, 2013 at 3:09 PM, Dániel Kehl <kehld at ktk.pte.hu> wrote:
> 
>> Looks like homework.
>>
>> Try ?qnorm
>> ________________________________________
>> Feladó: r-help-bounces at r-project.org [r-help-bounces at r-project.org] ;
>> meghatalmazó: Johannes Radinger [johannesradinger at gmail.com]
>> Küldve: 2013. december 12. 14:56
>> To: R help
>> Tárgy: [R] Solving a normal distribution pnorm for q
>>
>> Hi,
>>
>>
>>
>> I found follwowing example of pnorm here:
>>
>>
>> http://www.r-tutor.com/elementary-statistics/probability-distributions/normal-distribution
>>
>>
>>
>> Problem
>>
>> Assume that the test scores of a college entrance exam fits a normal
>> distribution. Furthermore, the mean test score is 72, and the standard
>> deviation is 15.2. What is the percentage of students scoring 84 or more in
>> the exam?
>>
>>
>>
>> Solution
>>
>>> pnorm(84, mean=72, sd=15.2, lower.tail=FALSE)
>>
>> [1] 0.21492
>>
>>
>>
>> That is straight forward, however what if I want to know the score the best
>> 30% students are reaching at least. So I know the solution of pnorm but
>> want to know its q. How can that be achieved in R?
>>
>>
>>
>> Any suggestions?
>>
>>
>>
>> /Johannes
>>
>>         [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
> 
> 	[[alternative HTML version deleted]]
> 
> 
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

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Eik Vettorazzi
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