[R] Help interpreting density().

Mark Difford
Tue, 29 Jul 2008 06:21:37 -0000

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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