Re: Example(s) of Biomodal distributions

Would this work?

m1 <- 3.5
m2 <- 6.5
s1 <- 0.8
s2 <- 0.8
dist1 <- dnorm(x, mean=m1, sd=s1)
dist2 <- dnorm(x, mean=m2, sd=s2)
biModalDist <- dist1 + dist2

q <- qnorm(.9,0,1)
z1 <- q*s1
z2 <- q*s2
zLow <- m1 - z1
zUp <- m2 + z

xShade <- seq(zLow, zUp, 0.1)
d1Shade <- dnorm(xShade, mean=m1, sd=s1)
d2Shade <- dnorm(xShade, mean=m2, sd=s1)
yShade <- d1Shade + d2Shade

windows()
plot(x, biModalDist, type="l")
polygon(x=c(zUp, zLow, xShade), y=c(0,0,yShade), col="gray")

On 1/15/2012 2:41 PM, AbouEl-Makarim Aboueissa wrote:
> Dear R users:
>
> I am currently teaching a course in Statistics. Can someone give an R code(s) to create a biomodal curve(s)
with shaded area of 90% and with 5% in each tail

Re: Example(s) of Biomodal distributions

x didn't make it through the cut-and-paste, it should be:

x <- seq(0, 10, 0.1)

also zUp has a typo, it should be:

zUp <- m2 + z2

That should work now.

On 1/15/2012 2:41 PM, AbouEl-Makarim Aboueissa wrote:
> Dear R users:
>
> I am currently teaching a course in Statistics. Can someone give an R code(s) to create a biomodal curve(s)
with shaded area of 90% and with 5% in each tail
>
> With many thanks
> abou
>
>
>
> ==========================
> AbouEl-Makarim Aboueissa, Ph.D.
> Associate Professor of Statistics
> Graduate Program Coordinator
> Department of Mathematics&  Statistics
> University of Southern Maine
> 96 Falmouth Street
> P.O. Box 9300
> Portland, ME 04104-9300

Re: Example(s) of Biomodal distributions

I recently wrote a function for the mosaic package that makes it easy  
to generate various kinds of plots of distributions.  For example, to  
plot a Binom(30,.35) distribution, you just use:

distPlot("binom",params=list(size=30, prob=.35))

and get the attached plot (if it makes it through to the list).

Additional arguments let you choose between different kinds of plots  
(density, histogram, qq, cdf), and there is a heuristic to guess  
whether the distribution is discrete or continuous and to the right  
thing.

I didn't set these up to make it easy to add the shading, but I think  
I could modify things to make that possible too.   Stay tuned.

---rjp

On Jan 15, 2012, at 2:41 PM, AbouEl-Makarim Aboueissa wrote:

> Dear R users:
>
> I am currently teaching a course in Statistics. Can someone give an  
> R code(s) to create a biomodal curve(s) with shaded area of 90% and  
> with 5% in each tail
>
> With many thanks
> abou

Re: Example(s) of Biomodal distributions

I have modified the distPlot() function in the mosaic package so that  
the following makes the desired plot (as a density histogram):

distPlot( "binom", params=list(35,.25), groups= y <  
dbinom(qbinom(0.05, 35, .25), 35,.25), kind='hist')

The groups argument is used to get the desired shading of tail  
probabilities.  (Technically, it is not shading 5% in each tail, but  
it is doing one of the reasonable approximations to that).

I expect this feature will show up on github sometime Monday (along  
with some other updates scheduled for release) and on CRAN in the near  
future.

If you are really anxious, you can get it from my personal repository  
using

	install.packages('mosaic', repos='http://www.calvin.edu/~rpruim/R',  
type='source')

Since images don't go through on the mailing list, I've placed a few  
here:

	http://www.calvin.edu/~rpruim/R/distPlot.pdf

---rjp

On Jan 15, 2012, at 2:41 PM, AbouEl-Makarim Aboueissa wrote:

Re: Example(s) of Biomodal distributions

Just noticing that I read the post below too quickly and thought it  
said "binomial" rather than "bimodal".  But my solution works all the  
same, you just need to provide a bimodal distribution as the first  
argument.  The only requirement is that if the name of your  
distribution is "foo", then dfoo, pfoo, and qfoo need to exist and do  
the correct things.  They may be user defined functions.

You can of course, use the groups argument however you like to define  
the tails of the distribution.  For example, something like

	groups = ( x < qfoo(0.05, ....) | x > qfoo(0.95) )

should shade the tails differently from the center.

In view of the email from Jeff Laux, I might consider adding some  
utilities to build new dfoo, pfoo, and qfoo functions from existing  
ones, at least for a few easy cases, like linear combinations.  That  
would make it really easy to generate various bimodal distributions.

---rjp

On Jan 15, 2012, at 2:41 PM, AbouEl-Makarim Aboueissa wrote:

> Dear R users:
>
> I am currently teaching a course in Statistics. Can someone give an  
> R code(s) to create a biomodal curve(s) with shaded area of 90% and  
> with 5% in each tail
>

Re: Example(s) of Biomodal distributions

Dear Abou,
I think Your trouble can be solved like there 
http://www.talkstats.com/showthread.php/11746-Problem-with-plotting-in-R

---
Zhan Chubukou
Chair of Pathological Physiology magistrant
Gomel State Medical University
Belarus