NavList:

   

Reply

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 , send email to NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---

   

Reply