# 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:

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_
> 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.
>
> 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
>>> > 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.-tp18704955p18706154.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
>>> 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
>> 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
> 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
> 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
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