# NavList:

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

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Re: Kurtosis, Gaussian distribution and leptokurtotic
From: Peter Fogg
Date: 2010 Dec 31, 15:00 +1100
Earlier I wrote:
"... because the population is so small a significantly non-Gaussian distribution or a leptokurtotic event, if this is the jargon you prefer, is always going to be likely."

Although not inevitable.  It all depends on the pattern formed by a particular set of sights, as influenced by the conditions of observation.

However, you won't know whether any particular round of sights could be later defined as having a standard distribution or not, UNTIL YOU PLOT THEM!

Obvious, innit?

On Fri, Dec 31, 2010 at 2:03 PM, Peter Fogg wrote:

Having informed myself (when you're looking for a helping hand its always waiting there, right at the end of your arm) that a "Gaussian distribution" is quite simply a standard distribution, and that positive kurtosis appears to be simply the opposite, and that leptokurtotic boils down to excessive positive kurtosis (however that is defined) I may now make so bold as to comment on the relevance of this jargon to the slope.

I guess we all know now what slope means; a methodology for the evaluation of a series of sights taken over a short period, but for the sake of anyone who may have tuned in recently, first a short diversion as to why the observation period must be short.

Its because drawing the calculated (=real) slope as a straight line is an approximation of a short portion of an arc (same as position lines).  The extent of curve of that arc varies with the position of the body in the sky, but as a practical 'rule of thumb' the maximum period of time is assumed to be 5 minutes (for star/planet sights at dawn or dusk the available window of opportunity is, of course, another time-limiting factor).

Therefore the number of timed sights that can be recorded is limited by those 5 available minutes (mind you, if other factors allow you can go on taking sights then choose the 5-minute period you prefer - perhaps avoiding altogether any apparent outliers).

How many timed sights can you record in 5 minutes?  If I have to record them myself its about 4 to 6, thus roughly one per minute - others may be faster.  If I have a scribe then more, and I have posted here an example of 9 sights.

The relevance of this to whether the distribution is standard or not lies in the disproportionate effect 1 or 2 outliers can have.  If both outliers lie to the same side of the slope, as they do in my 9-sight example, then they could lead to significant error if averaged blindly, and to adoption of a significantly erroneous slope if this is derived via linear regression.

In other words, because the population is so small a significantly non-Gaussian distribution or a leptokurtotic event, if this is the jargon you prefer, is always going to be likely.

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