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    Re: Real accuracy of the method of lunar distances
    From: Trevor Kenchington
    Date: 2003 Dec 31, 08:34 +0000

    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
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
                          Science Serving the Fisheries

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