[R] Help interpreting density().

[Bill.Venables at csiro.au]

In general there is no relation.  The output of density gives you
something you can plot, essentially.  So the x-values are simply a
series of points covering the range of the density and the y values are
the ordinates at those abscissae.

try

plot(density(rnorm(1000)^2)))

for example.


Bill Venables
CSIRO Laboratories
PO Box 120, Cleveland, 4163
AUSTRALIA
Office Phone (email preferred): +61 7 3826 7251
Fax (if absolutely necessary):  +61 7 3826 7304
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mailto:Bill.Venables at csiro.au
http://www.cmis.csiro.au/bill.venables/ 

-----Original Message-----
From: rkevinburton at charter.net [mailto:rkevinburton at charter.net] 
Sent: Tuesday, 29 July 2008 6:09 PM
To: r-help at r-project.org; Venables, Bill (CMIS, Cleveland)
Subject: RE: [R] Help interpreting density().

Sorry, poor example. I started with normal deviates and jumped without
thinking to Poisson. The main crux of the question is how does the
output of density relate to the parameters that describe some of the
standard distributions (mean and std for normal, lambda for Poisson, n
and p for Binomial, alpha and beta for Beta, etc.).

Thank you.

Kevin

---- Bill.Venables at csiro.au wrote: 
> You should read the documentation more carefully.  The bw is not
> "essentially the sd".  To quote the documentation the bw is "the
> smoothing bandwidth to be used. The kernels are scaled such that this
is
> the standard deviation of the smoothing kernel."  That is a very
> different thing.
> 
> You are confusing the standard deviation of the distribution with the
> standard deviation of the gaussian smoothing kernels.  
> 
> In the second case, density(rpois(1000, 0)), you are getting the
kernel
> density for a sample of 1000 zeros.  So there is just one distinct
> smoothing kernel and the bw is a default used for this case.  If you 
> 
> plot(density(rpois(1000, 0)))
> 
> you will see what that smoothing kernel looks like.
> 
> 
> Bill Venables
> CSIRO Laboratories
> PO Box 120, Cleveland, 4163
> AUSTRALIA
> Office Phone (email preferred): +61 7 3826 7251
> Fax (if absolutely necessary):  +61 7 3826 7304
> Mobile:                         +61 4 8819 4402
> Home Phone:                     +61 7 3286 7700
> mailto:Bill.Venables at csiro.au
> http://www.cmis.csiro.au/bill.venables/ 
> 
> -----Original Message-----
> From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org]
> On Behalf Of rkevinburton at charter.net
> Sent: Tuesday, 29 July 2008 2:15 PM
> To: r-help at r-project.org
> Subject: [R] Help interpreting density().
> 
> I issue the following:
> 
> > d <- density(rnorm(1000))
> > d
> 
> and get:
> 
> Call:
>         density.default(x = rnorm(1000))
> 
> Data: rnorm(1000) (1000 obs.);  Bandwidth 'bw' = 0.2235
> 
>        x                 y            
>  Min.   :-3.5157   Min.   :2.416e-05  
>  1st Qu.:-1.6892   1st Qu.:1.129e-02  
>  Median : 0.1373   Median :7.267e-02  
>  Mean   : 0.1373   Mean   :1.367e-01  
>  3rd Qu.: 1.9639   3rd Qu.:2.693e-01  
>  Max.   : 3.7904   Max.   :4.014e-01  
> 
> The documentation indicates that the bw is essentially the sd. Yet I
> have specified an sd of 1? How am I to interpret the ranges of the
> values? x ranges almost from -4 to +4 and y ranges from 0 to 0.4. The
> mean x is .1 which isn't too awfully close to what I would expect
(0.0).
> Then there is:
> 
> > d <- density(rpois(1000,0))
> > d
> 
> Call:
>         density.default(x = rpois(1000, 0))
> 
> Data: rpois(1000, 0) (1000 obs.);       Bandwidth 'bw' = 0.2261
> 
>        x                 y          
>  Min.   :-0.6782   Min.   :0.01979  
>  1st Qu.:-0.3391   1st Qu.:0.14073  
>  Median : 0.0000   Median :0.57178  
>  Mean   : 0.0000   Mean   :0.73454  
>  3rd Qu.: 0.3391   3rd Qu.:1.32830  
>  Max.   : 0.6782   Max.   :1.76436  
> 
> Here I am getting the mean that I expect from a Poisson distribuition
> but y ranges from 0 to 1.75. Again I am not sure what these numbers
> mean. How can I map the output to the standard distirbution
description
> parameters?
> 
> Thank you.
> 
> Kevin
> 
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