# Re: [R] Help interpreting density().

From: <rkevinburton_at_charter.net>
Date: Tue, 29 Jul 2008 00:52:34 -0700

OK. Thank you for pointing out my mistake.

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
> >
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> > and provide commented, minimal, self-contained, reproducible code.
> >
> >
>
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