Re: [R] Help interpreting density().

From: <Bill.Venables_at_csiro.au>
Date: Tue, 29 Jul 2008 16:12:56 +1000

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

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-----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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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. Received on Tue 29 Jul 2008 - 06:16:50 GMT

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