[R] Help interpreting density().

[Mark Difford]

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.
>> > 
>> > 
>> 
>> -- 
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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.
> 
> ______________________________________________
> 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.
> 
> 

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