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    Re: On LOPs
    From: Herbert Prinz
    Date: 2002 Apr 16, 18:02 +0000

    Thank you for the clarification. I was already getting worried that I would have
    to dig out my old statistics book from the basement. It is buried there for a
    reason, together with other dreadful books.
    I would like to ask you a favour. The images in pp1.gif and pp2.gif in your
    message from 04/16 show beautifully the spatial relation of confidence ellipse and
    cocked hat. I assume that you are showing 95% ellipses. With this assumption, it
    looks very reasonable that the confidence level of the entire hat should be 25%.
    It also gives an idea of the variation of probability density within the hat.
    Could you redraw these two images again, this time with a 25% confidence ellipse,
    and post it? Thank you in advance.
    Steven Tripp wrote:
    > On 4/16/02 11:39 AM, "Herbert Prinz"  wrote:
    > > Steven,
    > >
    > > Could  you please explain to us why the size of the confidence ellipse would
    > > depend in part on the angles that the three LOPs cross at?
    > I was wrong.
    > After playing with my program a little I see that the size can actually get
    > smaller with acute angles, provided that the intercepts (in the navigation
    > sense) are similar.  It can also get larger if the intercepts are (somewhat)
    > different.
    > Here are three examples.
    > 1. azimuths: 0, 60,120, intercepts: -2, 5, -1
    > 2. azimuths: 0, 110,120 ints: same
    > 3. azimuths: 110, 60, 120  ints: same
    > Note that two lines are the same in all plots.
    > In #2 the error in the NE-SW direction increases, but is a little less in
    > the NW-SE direction.
    > In #3 error is reduced in all directions.
    > Steve Tripp
    >   ------------------------------------------------------------------------
    >               Name: pp2.gif
    >    pp2.gif    Type: GIF Image (image/gif)
    >           Encoding: base64
    >               Name: pp1.gif
    >    pp1.gif    Type: GIF Image (image/gif)
    >           Encoding: base64
    >               Name: pp3.gif
    >    pp3.gif    Type: GIF Image (image/gif)
    >           Encoding: base64

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