Re: [R] Help interpreting density().

From: Mark Difford <mark_difford_at_yahoo.co.uk>
Date: Tue, 29 Jul 2008 01:42:32 -0700 (PDT)

Hi Kevin,

Clicking on the link I sent gets me there (?), though things are pretty slow at the moment. Perhaps try this related link, and from it get back to the first one:

http://en.wikipedia.org/wiki/Density_estimation

You can also get to this via histogram, so search for that in Wiki, and then...

HTH, Mark.

rkevinburton wrote:
>
> Sorry I tried WikiPedia and only found:
>
> Wikipedia does not have an article with this exact name.
>
> I will try to find some other sources of information.
>
> Kevin
>
> ---- Mark Difford <mark_difford_at_yahoo.co.uk> wrote:

>> 

> Hi Kevin,
>
>>> I still have my original question. How does the output relate to
>>> estimating the parameters 
>>> of a given density? I read that for a gausian kernal:

>
> This isn't the place for such questions: you need to do some _basic_
> reading
> on the subject so that you begin to understand something about the method
> you are messing about with. Basically (very basically) it's a smoothed out
> histogram. And you will probably (?) know that a histogram is [still used]
> to show you how a set of univariate data (random variable) is distributed.
>
> Perhaps start with http://en.wikipedia.org/wiki/Kernel_density, then go
> somewhere else. But since you have access to the web you really should
> have
> found something like this yourself.
>
> Regards, Mark.
>
>
> rkevinburton wrote:
>> 
>> OK. Thank you for pointing out my mistake.
>> 
>> I still have my original question. How does the output relate to
>> estimating the parameters of a given density? I read that for a gausian
>> kernal:
>> 
>> bw.nrd0 implements a rule-of-thumb for choosing the bandwidth of a
>> Gaussian kernel density estimator. It defaults to 0.9 times the minimum
>> of
>> the standard deviation and the interquartile range divided by 1.34 times
>> the sample size to the negative one-fifth power (= Silverman's ‘rule of
>> thumb’
>> 
>> But how does that relate to say a Poisson distribution or a two-parameter
>> distribution like a normal, beta, or binomial distribution?
>> 
>> Thank you.
>> 
>> Kevin
>> 
>> ---- Mark Difford <mark_difford_at_yahoo.co.uk> wrote: 
>>> 
>>> Hi Kevin,
>>> 
>>> >> The documentation indicates that the bw is essentially the sd.
>>> >> > d <- density(rnorm(1000))
>>> 
>>> Not so. The documentation states that the following about "bw": "The
>>> kernels
>>> are scaled such that this is the standard deviation of the smoothing
>>> kernel...," which is a very different thing.
>>> 
>>> The default bandwidth used by density is ?bw.nrd0. Read that
>>> documentation
>>> carefully and all might be clear.
>>> 
>>> HTH, Mark.
>>> 
>>> 
>>> rkevinburton wrote:
>>> > 
>>> > 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
>>> > 
>>> > ______________________________________________
>>> > 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.
>>> > 
>>> > 
>>> 
>>> -- 
>>> View this message in context:
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>>> 
>>> ______________________________________________
>>> R-help_at_r-project.org mailing list
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>>> PLEASE do read the posting guide
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>> 
>> ______________________________________________
>> 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.
>> 
>> 

>
> --
> View this message in context:
> http://www.nabble.com/Help-interpreting-density%28%29.-tp18704955p18707522.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> 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.
>
> ______________________________________________
> 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.
>
>
-- 
View this message in context: http://www.nabble.com/Help-interpreting-density%28%29.-tp18704955p18707787.html
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