# [R] Overlaying graphs

Spencer Graves spencer.graves at pdf.com
Thu Sep 4 16:34:27 CEST 2003

```	  Your observation that qqnorm "does not appear to be very general" is
rebutted by Venables and Ripley (2002) Modern Applied Statistics with S,
4th ed. (Springer, p.108):  "One of the best ways to compare the
distribution of a sample x with a distribution is to use a Q-Q plot. ...
This idea can be applied quite generally.  For example, to test a sample
against a t9 distribution, we might use

plot( qt(ppoints(x), 9), sort(x) )

Before I consider the "best-fitting probability distribution", I want
to know something about the nature of the application and what the
numbers claim to represent:  If they are discrete counts, I will not
even consider a normal distribution except as an approximation.  If they
are money or physical measurements like power or grams in applications
where they should never be negative, then I may want to take logarithms
first before I do anything else.  If lifetime data, I will consider
lognormal and Weibull, and prepare a cumulative hazard plot before doing
much else.  If a normal probability plot shows skewness, I will look for
another distribution or a transformation that makes sense with the
application.  If it shows discontinuities, I will consider mixtures.  By
the time you start considering mixtures, the number of alternative
distributional models becomes infinite.

hope this helps.  spencer graves

Paul Meagher wrote:
> My apologies for the last email that only contained the message and not my
> reply.  Here is what I meant to send.
>
> ----- Original Message -----
> From: "Richard A. O'Keefe" <ok at cs.otago.ac.nz>
> To: <paul at datavore.com>
> Sent: Thursday, September 04, 2003 2:56 AM
> Subject: Re: [R] Overlaying graphs
>
>
>>I do not know how to overlay the curve graphic on top of hist graphic.
>>
>
>
> I learned about it from one of the list members and it worked ok for me.
> This is the recipe I finally came up with:
>
> mu   <- mean(fat\$height)
> sdev <- sd(fat\$height)
> par (fin=c(4,4))
> hist(fat\$height, br=20, freq=FALSE, col="lightblue",
>      border="black", xlab="Male Height in Inches",
>      main = paste("Histogram of" , "Male Height"))
> curve(dnorm(x, mu, sdev), add=TRUE, from=64, to=78, col="red", lwd=5)
>
>
>>I am hoping to show visually that the normal curve overlays the obtained
>>probability distribution when plotted on the same graph.  Unfortunately, I
>>an not sure how to overlay them. Can anyone point me in the right
>
> direction
>
>>or show me the code.
>>
>>This is a bad way to do it anyway.  What you want is a qqnorm plot.
>>See ?qqnorm.
>
>
> Yes qqnorm looks like a better tool for this particular job.  It does not
> appear to be very general in the sense that you could visually inspect
> whether poissson distributed data conforms to a theoretical poisson
> distribution.
>
> I guess this leads to two more questions:
>
> 1. Is the Anderson-Darling goodness-of-fit test the recommended analytic
> test for determining whether a normal distribution conforms to a theoretical
> normal distribution.
>
> 2. Does R have a suite of "best-fit" tools for finding the best
> fitting-probability distribution for any observed probability distribution?
>
> Regards,
> Paul Meagher
>
>
>
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