🚀 go-pugleaf

Darren O'Shaughnessy <dos105@rsphy2.anu.edu.au> writes:
>   I would have expected the distribution of the darts to be approximately
>normal, but it appears that the distribution is flatter on top than a
>Gaussian curve with the same standard deviation, hence with relatively more
>darts falling around the one s.d. area.

Perhaps you should define what you mean by "the distribution of the
darts."  The distribution is obviously two-dimensional, but your other
comments sound like you are dealing with a one-dimensional distribution.
I don't know, for example, what "around the one s.d. area" means for
your two-dimensional distribution.

If you are looking at just the distance from the center as the
statistic, then if the distribution of the dart locations were Gaussian,
the probability distribution of the distance would definitely not be
Gaussian (nor half-Gaussian).

                                        David desJardins

In article <dos105-130992174724@150.203.49.43>, dos105@rsphy2.anu.edu.au
(Pat Rourke) wrote:
> 
>    I'm working on a darts simulation program, and so have studied the
> distribution of darts aimed at the bull by myself (an amateur player who
> gets perhaps one in five or six inside the 25-ring).
>    I would have expected the distribution of the darts to be approximately
> normal, but it appears that the distribution is flatter on top than a
> Gaussian curve with the same standard deviation, hence with relatively more
> darts falling around the one s.d. area.
>    At the moment, I can model this by convoluting a uniform distribution
> with a normal distribution of similar variance - i.e. by assuming that the
> normal errors are overlaid upon a uniformly-random bias. Can anyone think
> of a more natural distribution which "looks" like this, and can be related
> back to the original sources of the throwing inaccuracies (my swinging arm,
> my eyes, my poor pressured mind ...)?
>    Thanking you in advance of a possible discussion, depending on the
> overlap of statisticians and dart-players in the population of course.

    For the sake of clarity, the following:
     I am, in fact, treating the radial distance as the normally
distributed variable, with the angle uniformly randomly chosen. I then have
the option of "stretching" the distribution vertically to take account of
the fact that this is the source of more error for experienced players than
the lateral motion of the arm. However, at this stage I have assumed that
the distribution is circularly, rather than elliptically, symmetric.
   Thanking you for communication so far,

              Pat Rourke  (you may not have heard of me)