# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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 suggest. 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. -FER --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---