R help - Sep 2008 - densities with overlapping area of 0.35

Hi,

I like to generate two normal densities such that the overlapping area
between them is 0.35. Is there any code/package available in R to do that??

Regards,

Lavan
-- 
View this message in context:
http://www.nabble.com/densities-with-overlapping-area-of-0.35-tp19384741p19384741.html
Sent from the R help mailing list archive at Nabble.com.

Let X be normally distributed with mean 0 and let f be it's density. Now the
density of X+a will be f shifted right by a. Since the density is symmetric
around mean it follows that the area of overlap of the two densities is exactly
P(X>a) + P(X<-a).
So if X~N(0,1), we want P(X>a) + P(X<-a) = 2P(X<-a) = 0.35, so
P(X<-a) = 0.175 which yields -a =  qnorm(0.175) = -0.9345893, so a =
0.9345893.


--- On Tue, 9/9/08, Lavan <rsumithran at yahoo.com> wrote:
> From: Lavan <rsumithran at yahoo.com>
> Subject: [R]  densities with overlapping area of 0.35
> To: r-help at r-project.org
> Received: Tuesday, 9 September, 2008, 12:11 PM
> Hi,
> 
> I like to generate two normal densities such that the
> overlapping area
> between them is 0.35. Is there any code/package available
> in R to do that??
> 
> Regards,
> 
> Lavan
> -- 
> View this message in context:
>
http://www.nabble.com/densities-with-overlapping-area-of-0.35-tp19384741p19384741.html
> Sent from the R help mailing list archive at Nabble.com.
> 
> ______________________________________________
> 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.

Hi,

I just findout that the KL Divengence depends on the variances of the
distrubutions too and I'm trying to figureout how to do this. please help
me.

let's say 

X ~n(0,1) and Y~n(2*a, sigma^2). Is there any way I can calculate the
"sigma" and "a" corresponding to an overlapping area of
0.35.

Thank you,

Lavan



Lavan wrote:
> 
> Hi,
> 
> I like to generate two normal densities such that the overlapping area
> between them is 0.35. Is there any code/package available in R to do
> that??
> 
> Regards,
> 
> Lavan
> 
-- 
View this message in context:
http://www.nabble.com/densities-with-overlapping-area-of-0.35-tp19384741p19404352.html
Sent from the R help mailing list archive at Nabble.com.