NavList:

   

Reply

I wrote earlier:
"So you're saying these observations exhibit excess kurtosis "

And you replied:
"Let us stick to simple language:-)"

Well, you said that the distribution of the observations has more weight in
the tails than a common normal distribution. Apart from the very colloquial
"fat tailed distribution", the only name for this is kurtosis. I certainly
agree with you that it is something that you should worry about when you're
dealing with distributions of real-world data. Almost all data which is said
to be approximately normally distributed does, in fact, show some kurtosis
if you study it long enough. This is responsible for all sorts of crazy
misunderstandings in divers fields. For example, if you were to study price
changes in currency exchange rates, you could easily calculate a standard
deviation, and based on that you might predict that the odds of a three
standard deviation move are something like 300-to-1 against. But if you then
look at the data again and COUNT the number of moves of that size
historically, you discover that the odds of a large move are considerably
larger. In other words, outliers are much more common than a normal
distribution would suggest. A currency trader who ignores this fact can get
into some mighty serious trouble (have a look at a brief article called
"Kurtosis Risk" on Wikipedia for another take on this). For the navigator,
the same issue can arise. If results tend to cluster near a mean, you still
should worry that there may be some aspect of your observations, or your
sextant's behavior, or the nature of the observation itself, that leads to a
greater than expected number of outlying points. BUT, and this is a BIG BUT,
it is fairly easy to imagine that there are more outliers than normal when
you worry about them too much. The only RELIABLE measure is a direct
calculation of the sample kurtosis, and fortunately, most modern
spreadsheets can do this easily. If it's not significantly above zero
('significantly' has to be defined), then you cannot claim that the
distribution has "fat tails". White's observations do NOT show significant
kurtosis.

I wrote:
"Enter those values into an Excel spreadsheet."

And you replied:
"I did! And wrote about this to the list 4 (four) times. Are my messages get
lost?? You can see the results on
www.math.purdue.edu/~eremenko/accuracy.html"

No, Alex, your messages are not getting "lost". Let's not go through that
again. You can easily check to see if your messages are distributing by
looking for them in the list archive at http://www.navlist.net. And yes, I
did look at your bar graphs. Thanks for making them.

Also, please note that I spelled out detailed instructions because in any
conversation on this list, even if it seems that it is a conversation
between two people, there are often other people reading along, other people
who may want to participate, so in general, I try to give instructions "as
if" the other person is not 100% familiar with what we're discussing. So,
YES, I know you had already entered the data in a spreadsheet. But I also
note that your web page does not include any values for standard deviation
or kurtosis

And then you asked:
"Look at these error distributions. If you do not want to look at other
results out of principle, look at White's results plotted. And then tell us:
on your opinion, does this plot confirm that "one can measure a distance
with 0'2 accuracy, reliably"."

White's observations show a standard deviation on individual observations
(which may be multiple actual sights or may be single sights) of 0.25
minutes of arc. And if ew average sets of four, the s.d. drops to about 0.1
minutes of arc. That means that about 68% will lie within one standard
deviation of zero error. Whether that fits your definition of the word
"reliably" is up to you. White's observations also show no significant
kurtosis. There are no "extra" outliers, no evidece of a non-normal sample.

Of course, at some point there almost have to be highly non-normal outliers
in sextant observations. So-called "blunders", like writing down 20 degrees
for 30 degrees, count as errors but the odds against them would be
millions-to-one (or worse!) if we believed all recorded sextant observations
obeyed a true normal distribution. So as I said at the top, I agree with you
that we should be on the lookout for outliers. This applies to all celestial
navigation, whether it's Noon Sun latitudes or intercepts for LOPs or time
sights. There's nothing special about lunars on this score.


In another post, replying to Henry, you wrote:
"This I consider a violation of the rules:-) If one chooses this way, then
why not to use
a 20x scope, and a theodolite, or some other instrument more accurate than a
sextant, after all?"

Well, because some people shoot lunars for other reasons, and I think this
is worth remembering. For a long time, I thought that you personally, Alex,
were shooting lunars because you wanted to determine the arc error of your
instrument. If that's the case --and it is for some people who play this
"game"-- then mounting the instrument on a stand (maybe an old telescope
mount with a clock drive) and attaching a more powerful telescope to the
sextant might very well count as "playing by the rules".

And you wrote:
"My ultimate interest is in the measurement at sea. Unfortunately I have no
possibility to sail very frequently."

Yeah, I think we should find a corporate sponsor! Buy us a couple of berths
aboard a nice tall ship for five or six of us, first-class cabins would be
nice, and sail us around the world for a year so we can get some good hard
data on lunars... Aahhh...

 -FER


--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to NavList@navlist.net
To , send email to NavList-@navlist.net
-~----------~----~----~----~------~----~------~--~---

   

Reply