# [R] t-distribution

Nair, Murlidharan T mnair at iusb.edu
Fri Aug 3 16:46:02 CEST 2007

```I am trying to shade the critical regions for normal distribution with
different means and making overlaps of the plots to explain Type I and
Type II errors. I tried the following. If I calculate the z score and as
I did below, can I use it to pick regions from the original data? I
think I am making mistake by calculating the z scores for d\$x, can
someone explain the mistake I am making?

left<- -1.96
right<- 1.96
mu1<-rnorm(100000,20,5)
d<-(density(mu1))
x.tmp<-d\$x
y.tmp<-d\$y
x<-x.tmp
y<-y.tmp
mu1z<-(x.tmp-mean(x.tmp))/sd(x.tmp) # is it correct?
a<-which(mu1z <=left)
b<-which(mu1z >=right)
plot(x.tmp,y.tmp, type="l")
polygon(x=c(x.tmp[a],rev(x.tmp[a])),y=c(y.tmp[a],rep(0,length(y.tmp[a]))
),col="gray90")
polygon(x=c(x.tmp[b],rev(x.tmp[b])),y=c(y.tmp[b],rep(0,length(y.tmp[b]))
),col="gray90")

-----Original Message-----
From: Stephen Tucker [mailto:brown_emu at yahoo.com]
Sent: Thursday, August 02, 2007 3:11 PM
To: Nair, Murlidharan T; r-help at stat.math.ethz.ch
Subject: RE: [R] t-distribution

yes, or

p <- seq(0.001,0.999,,1000)
x <- qt(p,df=9)
y <- dt(x,df=9)
plot(x,y,type="l")

f <- function(x,y,...) {
polygon(x=c(x,rev(x)),y=c(y,rep(0,length(y))),...)
}
with(data.frame(x,y)[x >= 2.3,],f(x,y,col="gray90"))
with(data.frame(x,y)[x <= -2.3,],f(x,y,col="gray90"))

--- "Nair, Murlidharan T" <mnair at iusb.edu> wrote:

>
> I tried doing it this way.
>
> left<--2.3
> right<-2.3
> p <- seq(0.001,0.999,,1000)
> x <- qt(p,df=9)
> y <- dt(x,df=9)
> plot(x,y,type="l")
> x.tmp<-x
> y.tmp<-y
> a<-which(x<=left)
>
polygon(x=c(x.tmp[a],rev(x.tmp[a])),y=c(y.tmp[a],rep(0,length(y.tmp[a]))
),col="gray90")
> b<-which(x>=right)
>
polygon(x=c(x.tmp[b],rev(x.tmp[b])),y=c(y.tmp[b],rep(0,length(y.tmp[b]))
),col="gray90")
>
> Thanks ../Murli
>
>
>
> -----Original Message-----
> From: Richard M. Heiberger [mailto:rmh at temple.edu]
> Sent: Thu 8/2/2007 10:25 AM
> To: Nair, Murlidharan T; Stephen Tucker; r-help at stat.math.ethz.ch
> Subject: Re: [R] t-distribution
>
> I believe you are looking for the functionality I have
> in the norm.curve function in the HH package.
>
>
> example(norm.curve)
>
>

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