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Jan,

Another point for you to consider:

You wrote: "you can be statistically sure that your error won't exceed
the value of (SE times 3) in 99,7% of observations". You can only be
sure of that if the errors in your observations are "Normally"
distributed (which is to say that they follow a Gaussian distribution).
This sort of "Normal" distribution is not normal at all (at least not
with the biological systems I get to run statistical analyses on). If
you are estimating the standard deviation as 1/0.6745 times your
"probable error", oddities of the error distribution may not matter that
much but once you start pushing out to the 99th percentile, even minor
oddities would matter a lot.

I'm not going to try guessing at the distribution of the error term in
an overall estimate of GMT derived from a lunar observation but I do
suspect that it has truncated ends. That is: I suspect that a navigator
would discard any observation which led him to a position 45 minutes of
longitude away from his DR. At least, he would be very suspicious of it
and would repeat it next day, then adopt the second observation as the
more accurate one. (The chance of getting two lunars in succession, each
of which had a probability of 1-0.997 = 0.003 is of course 0.000009 or
about one in a million. If you are that unlucky, inaccurate lunars may
be the least of your problems!)


Trevor Kenchington



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Trevor J. Kenchington PhD                         Gadus@iStar.ca
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