R help - Mar 2012 - A question on histogram - area much less than 1

Hello,

   I have problem running the histogram function "hist". The area
under the
histogram is much lower than 1. Could anyone tell me what the problem is?
Thanks,
   (The total number of observation is 992 (close to 1000), so the
probability that 0<Y1<35 is approximately 0.277)

miao



rm(list=ls())
par(mfrow=c(1, 1))
Y <- cbind(matrix(35*0.5,1,277), matrix(35*1.5, 1, 146), matrix(35*2.5, 1,
99), matrix(35*3.5,1,80), matrix(35*4.5, 1, 69), matrix(35*5.5, 1, 63),
matrix(35*6.5, 1, 52), matrix(35*7.5,1, 53), matrix(35*8.5, 1, 55),
matrix(35*9.5, 1, 98))
Y1<-as.vector(Y)
par(mar=c(4.5, 4.1, 3.1, 0))
hist(Y1, breaks=seq(0, 350, by=35), ylim=c(0, 0.3), col="grey80",
freq=FALSE)
par(mar=c(5.1, 4.1, 4.1, 2.1))

	[[alternative HTML version deleted]]

Hi Miao,

With option freq=FALSE, the function hist calculates densities, i.e. in your
case,
counts/total/length in-between breaks.

h <- hist(Y1, breaks=seq(0, 350, by=35),freq=FALSE)



If you calculate:?
h$counts/sum(h$counts)/35 = h$density

Regards,
Pascal

----- Mail original -----
De?: jpm miao <miaojpm at gmail.com>
??: r-help at r-project.org
Cc?: 
Envoy? le : Lundi 12 mars 2012 16h42
Objet?: [R] A question on histogram - area much less than 1

Hello,

?  I have problem running the histogram function "hist". The area
under the
histogram is much lower than 1. Could anyone tell me what the problem is?
Thanks,
?  (The total number of observation is 992 (close to 1000), so the
probability that 0<Y1<35 is approximately 0.277)

miao



rm(list=ls())
par(mfrow=c(1, 1))
Y <- cbind(matrix(35*0.5,1,277), matrix(35*1.5, 1, 146), matrix(35*2.5, 1,
99), matrix(35*3.5,1,80), matrix(35*4.5, 1, 69), matrix(35*5.5, 1, 63),
matrix(35*6.5, 1, 52), matrix(35*7.5,1, 53), matrix(35*8.5, 1, 55),
matrix(35*9.5, 1, 98))
Y1<-as.vector(Y)
par(mar=c(4.5, 4.1, 3.1, 0))
hist(Y1, breaks=seq(0, 350, by=35), ylim=c(0, 0.3), col="grey80",
freq=FALSE)
par(mar=c(5.1, 4.1, 4.1, 2.1))

??? [[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.

Why do you say that the area is much lower than 1?
It is exactly equal to 1.

How did you calculate this area?

Your code seems extremely convoluted and confused.

You could construct your (rather bizarre) vector Y1 much
more simply as

Y1 <- rep((0.5 + 0:9)*35,c(277,146,99,80,69,63,52,53,55,98))

What do you think you are accomplishing via that call to par()
given *after* the plotting has been done?

Why set ylim to a value that is so incommensurate with the
heights of the histogram bars?

     cheers,

         Rolf Turner

On 12/03/12 20:42, jpm miao wrote:
> Hello,
>
>     I have problem running the histogram function "hist". The
area under the
> histogram is much lower than 1. Could anyone tell me what the problem is?
> Thanks,
>     (The total number of observation is 992 (close to 1000), so the
> probability that 0<Y1<35 is approximately 0.277)
Why are you approximating?  The empirical probability is exactly
equal to 277/992 = 0.2792339.
> miao
>
>
>
> rm(list=ls())
> par(mfrow=c(1, 1))
> Y<- cbind(matrix(35*0.5,1,277), matrix(35*1.5, 1, 146), matrix(35*2.5,
1,
> 99), matrix(35*3.5,1,80), matrix(35*4.5, 1, 69), matrix(35*5.5, 1, 63),
> matrix(35*6.5, 1, 52), matrix(35*7.5,1, 53), matrix(35*8.5, 1, 55),
> matrix(35*9.5, 1, 98))
> Y1<-as.vector(Y)
> par(mar=c(4.5, 4.1, 3.1, 0))
> hist(Y1, breaks=seq(0, 350, by=35), ylim=c(0, 0.3), col="grey80",
> freq=FALSE)
> par(mar=c(5.1, 4.1, 4.1, 2.1))

You expected the sum to be 1 and it is:
> a <- hist(Y1, breaks=seq(0, 350, by=35), col="grey80",
freq=FALSE)
> a$density*35
 [1] 0.27923387 0.14717742 0.09979839 0.08064516 0.06955645 0.06350806
 [7] 0.05241935 0.05342742 0.05544355 0.09879032
> sum(a$density*35)
[1] 1

Note that the first density multiplied by 35 is .279 exactly what you
expected and the sum of the densities multiplied by the width of each bar
(35) is 1. The height of the bar is not the probability, the area of the bar
is the probability.

----------------------------------------------
David L Carlson
Associate Professor of Anthropology
Texas A&M University
College Station, TX 77843-4352

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Rolf Turner
> Sent: Monday, March 12, 2012 3:53 AM
> To: jpm miao
> Cc: r-help at r-project.org
> Subject: Re: [R] A question on histogram - area much less than 1
> 
> On 12/03/12 21:44, jpm miao wrote:
> > Hello,
> >
> >    Thanks very much for your kind response. Yes, if I multiply by the
> > width "35", the area should be equal to one.
> >
> >    How can I plot the probability bars rather than density bars? That
> > is, I would like the height of the first bar to be 0.279, which is
> the
> > probability that the variable falls between 0 and 35.
> 
> If you want probabilities rather than densities you should be using
> barplot() rather
> than histogram:
> 
> TBL <- table(Y1)
> barplot(TBL/sum(TBL))
> 
>      cheers,
> 
>          Rolf Turner
> 
> ______________________________________________
> 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.