NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: The Darn Old Cocked Hat - the sequel 1
From: Geoffrey Kolbe
Date: 2013 Mar 13, 19:03 +0000
From: Geoffrey Kolbe
Date: 2013 Mar 13, 19:03 +0000
Hanno...
I don't buy your maths. The problem you outline in your two 'papers' is very similar to the statistical distribution of the fall of shot at a target. The standard work on that is "Statistical Measures of Accuracy for Riflemen and Missile Engineers" by Frank E Grubbs. It was self published in 1964, but is still the seminal and most cited work on this subject. I suggest you glance in that work to see how your subject should be treated. I should add that ammunition factories around the world shoot millions of rounds of ammo every day and measure the quality of their ammo using the statistical techniques laid out in Grubbs' monograph. If Grubbs was wrong, we would know about it!
Karl...
You said: "Compare the Goudsmit result of the true shipâs position being outside the hat 75% of the time, with the symmedian result. They are both correct results to two different questions (but only the last one is relevant for CN). It requires some intriguing thought to see why this is true."
Actually, the Goudsmit result can be achieved by averaging over the entire grand canonical ensemble of possible cocked hats within the probability distribution you describe, as was done by somebody using Monte Carlo methods (I forget who) the last time we went through this. The two approaches are equivalent.
Geoffrey Kolbe
I don't buy your maths. The problem you outline in your two 'papers' is very similar to the statistical distribution of the fall of shot at a target. The standard work on that is "Statistical Measures of Accuracy for Riflemen and Missile Engineers" by Frank E Grubbs. It was self published in 1964, but is still the seminal and most cited work on this subject. I suggest you glance in that work to see how your subject should be treated. I should add that ammunition factories around the world shoot millions of rounds of ammo every day and measure the quality of their ammo using the statistical techniques laid out in Grubbs' monograph. If Grubbs was wrong, we would know about it!
Karl...
You said: "Compare the Goudsmit result of the true shipâs position being outside the hat 75% of the time, with the symmedian result. They are both correct results to two different questions (but only the last one is relevant for CN). It requires some intriguing thought to see why this is true."
Actually, the Goudsmit result can be achieved by averaging over the entire grand canonical ensemble of possible cocked hats within the probability distribution you describe, as was done by somebody using Monte Carlo methods (I forget who) the last time we went through this. The two approaches are equivalent.
Geoffrey Kolbe
