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    Re: Lunar distance accuracy
    From: Frank Reed
    Date: 2007 Oct 27, 22:11 -0400

    Alex, you wrote:
    "a) distribution of errors is FAR from normal. Which means that the usual
    measures of dispersion cannot be applied.
    b) they are especially far from normal in their "tails".
    That is there are MORE LARGE ERRORS than a normal distribution would
    Indeed, in the 42 observations of White, we have one error of 0'.8 and 3
    errors of about 0'.5 in the distance."
    So you're saying these observations exhibit excess kurtosis (a leptokurtic
    distribution is the fancy name for "fat tails"). I would in fact contend
    that they show NO SUCH THING (not White's at least). Enter those values into
    an Excel spreadsheet. Excel has nice built-in stat functions including
    KURT(). Of course, you could use another stat package if you prefer. In
    Excel, you'll have a column filled with the values from White's article:
     -55, 11, 30, -35, ... -4, 37 (42 values in all). Then calculate the standard
    deviation and kurtosis for that column (e.g. STDEV(A1:A42), KURT(A1:A42)).
    You should find sd=30.6 and kurt=0.39. That is actually a rather low value
    for kurtosis excess, and it's not statistically significant. In other words,
    by the standard test, the data IS consistent with being drawn from a
    standard normal distribution. No "fat tails"! If you change the largest
    outlier in the dat from -96 to -88 (a very small change), then the kurtosis
    excess is almost exactly zero --a near-perfect normal distribution.
    But let's suppose you find that your observations of lunars DO show
    significant kurtosis. Well, it's not the end of the world. There are
    standard statistical procedures for dealing with these things. If you want
    to do simulations, just to get a feel for the behvior, a very nice way to
    model a distribution with significant kurtosis is to to create two normally
    distributed random number generators with different standard deviations,
    e.g. sd1=0.25, sd2=0.50. Then draw from the first distribution with
    probability phi, e.g.=90%, and draw from the second with probability 1-phi.
    And that will give you fat tails. Note that the real process does not have
    to have this two-sided nature. It's just a good simulation technique.
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