[R] R function for Probabilities for the (standard) normal distribution

[David Winsemius]

On Aug 19, 2009, at 7:04 AM, Rene wrote:

> Dear All,
>
> I need to write an R function which computes values of   
> Probabilities for
> the (standard) normal distribution, ¦µ(z) for z > 0 by summing this  
> power
> series. (We should accumulate terms until the sum doesn't change). I  
> also
> need to make the function work for vector of values z.

Two problems:
One, this appears to be a homework exercise.
>
> The initial fomular is
>
> ¦µ(z) = ( 1/ sqrt(2¦Ð) )* ¡Ò e^(-t^2/2)dt       (¡Ò is from -¡Þ, z)
>
>         = 1/ 2 + ( 1/ sqrt(2¦Ð) )* ¡Ò e^(-t^2/2)dt     (¡Ò is from 0  
> to z)

Two, you are posting in HTML mail and the characters that you may  
think we should be seeing reading as Greek letters including I presume  
capital sigma for summation are .... not displayed properly.
>
>
>
> I can substituting x = -t^2/2 into the series expansion for the  
> exponential
> function
>
> e^x = ¡Æ x^n/n!         (¡Æ is from n=0 to ¡Þ)
>
> I can obtain the series
>
> e^(-t^2/2) = ¡Æ (-1)^k*t^2k / 2^k*k!       (¡Æ is from n=0 to ¡Þ)
>
> This series can be integrated term by term to obtain the formula
>
> ¦µ(z) = 1/ 2 + ( 1/ sqrt(2¦Ð) ) * ¡Æ (-1)^k*z^(2k+1) / (2^k*k! *(2k 
> +1))
> (¡Æ is from n=0 to ¡Þ)
>
>
> I know how to write the R function for exponential function e^x
>
> expf  = function (x)
>
>                {
>
>                x=ifelse((neg=(x<0)),-x,x)
>
>                n=0;term=1
>
>                 oldsum=0; newsum=1
>
>                while(any(newsum != oldsum)) {
>
>                oldsum=newsum
>
>                n=n+1
>
>                term = term*x/n
>
>                newsum = newsum+term}
>
>                ifelse(neg, 1/newsum, newsum)
>
>                }
>
> I know it will be similar to the above coding, but I don¡¯t know  
> exactly how
> should we  modify the above coding in order to get Probabilities for  
> the
> (standard) normal distribution, ¦µ(z) for z > 0.
>
> Can anybody advise me on this??
>
> Thanks a lot.
>
> Rene.
> 	[[alternative HTML version deleted]]
>
> ______________________________________________

David Winsemius, MD
Heritage Laboratories
West Hartford, CT