# Wiki pages I created

Covering Circle Radius versus Extreme Spread - should be pretty good.

Projectile Dispersion Classifications - getting close...

Extreme Spread * measure

Figure of Merit * measure

Leslie 1993 - notion ok, disagree with content on page.

Measuring Precision - this is fairly solid.

Mean Radius * measure

Sighting a Weapon ** needs work

Stringing seems mostly ok. Fuzzy on how to handle inter/exterior ballastics.

What is ρ in the Bivariate Normal distribution? think this pretty good.

Interrelationship of the Range Measurements

• Range
• Studentized Range
• Covering Circle
• Diagonal
• ES
• FOM
• ES

--- Carnac the Magnificent

Suppose that Xk has the gamma distribution with shape parameter k∈(0,∞) and fixed scale parameter b∈(0,∞). Then the distribution of the standardized variable below converges to the standard normal distribution as k→∞:

$$Z_k = \frac{X_k−kb}{b\sqrt{k}}$$

Measurements

 Circular Error Probable - CEP(50) Experimental Summary Given Assumptions Data transformation Experimental Measure Outlier Tests Theoretical ES Distribution Circular Dispersion Parameters Needed PDF CDF Mode, Median, Mean, Standard Deviation, %RSD Sample Variance and Its distribution Outlier Tests Errors caused by Orthogonal Elliptical Dispersion Parameters Needed PDF CDF Mode, Median, Mean, Standard Deviation, %RSD Sample Variance and Its distribution Outlier Tests Errors caused by Nonorthogonal Elliptical Dispersion Parameters Needed PDF CDF Mode, Median, Mean, Standard Deviation, %RSD Sample Variance and Its distribution Outlier Tests See Also Circular Error Probable - CEP(50) Experimental Summary Given Assumptions Data transformation Experimental Measure (CEP(50) From Ranking) Outlier Tests CEP(50) From Fitting to Rayleigh distribution Parameters Needed PDF CDF Mode, Median, Mean, Standard Deviation, %RSD Sample Variance and Its distribution Errors Due to Orthogonal Elliptical Dispersion Due to Hoyt Dispersion Due to Fliers Outlier Tests Within a System Between Systems

1. Elliptical Error Probable
2. Experimental Summary
1. Given
2. Assumptions
3. Data transformation
4. Experimental Measure
5. Outlier Tests
3. Theoretical ES Distribution
1. Dispersion by Rayleigh Distribution
2. Dispersion by Orthogonal Elliptical Distribution
1. Parameters Needed
2. PDF
3. CDF
4. Mode, Median, Mean, Standard Deviation, %RSD
5. Sample Variance and Its distribution
6. Outlier Tests
3. Dispersion by Hoyt Distribution
1. Parameters Needed
2. PDF
3. CDF
4. Mode, Median, Mean, Standard Deviation, %RSD
5. Sample Variance and Its distribution
6. Outlier Tests

  "The difference between theory and practice is larger in
practice than in theory."

In theory there is no difference between theory and practice. But, in practice, there is.


sighting shot distribution

The Mean Radius is the average distance over all shots to the groups center.

Given
• set of n shots {$$(h_1, v_1), (h_2, v_2), ..., (h_n, v_n)$$}
for which all of the (h,v) positions are known
Assumptions
• Origin at $$(r,\theta) = (0,0)$$
• Rayleigh Distribution for Shots
• $$\sigma_h = \sigma_v$$
• $$\rho = 0$$
• $$PDF_{r_i}(r) = \frac{r}{\sigma^2}e^{-r^2/2\sigma^2}$$
• With conversion from Cartesian coordinates to Polar coordinates, $$\theta$$ will be entirely random and independent of radius
• No Flyers
Data Pretreatment Shot impact positions converted from Cartesian Coordinates (h, v) to Polar Coordinates $$(r,\theta)$$
• Origin translated from Cartesian Coordinate ($$\bar{h}, \bar{v}$$) to Polar Coordinate $$(r = 0, \theta = 0)$$
Experimental Measure $$\bar{r_n}$$ - the average radius of n shots

$$\bar{r_n} = \sum_{i=1}^n r_i / n$$
where $$r_i = \sqrt{(h_i - \bar{h})^2 + (v_i - \bar{v})^2}$$

$$PDF_{r_0}(r; n, \sigma)$$ $$\frac{nr}{\sigma^2}e^{-nr^2/2\sigma^2}$$
$$CDF_{r_0}(r; n, \sigma)$$ $$1 - e^{-nr^2/2\sigma^2}$$
Mode of PDF($$\bar{r_n}$$) $$\frac{\sigma}{\sqrt{n}}$$
Median of PDF($$\bar{r_n}$$) $$\frac{\sigma}{\sqrt{n}}\sqrt{ln{(4)}}$$
Mean of PDF($$\bar{r_n}$$) $$\frac{\sigma}{\sqrt{n}}\sqrt{\frac{\pi}{2}}$$
(h,v) for all points? Yes
NSPG Invariant No
Robust No

# master ref page

I like the structure of this wiki page. You can look at the "groups of papers" then jump to a specific paper and use the browser back button to go back to the group.

Could we make this the "master" reference page?

(1) Move references to top of page (2) put TOC that floats to right (3) Have level 1 headings for various topics (eg CEP Literature, EEP Literature, ES, Rayleigh Model, Hoyt Model) (4) Each level 1 heading would have various "groups" of papers. (5) From some paper that we want to discuss create an off page link for that paper. (eg comments on "prior Art" page

how I'd redo references so as to provide some that was "linkable" and could be "named"

So Blischke_Halpin_1966 could be name of wiki page and a "named" link within the page. thus reference in a wiki page would be something like:

: yada yada yada (Blischke_Halpin_1966) yada yada yada


the link would jump to the "master" page of references to that entry.

Blischke_Halpin_1966
Blischke, W. R., & Halpin, A. H. (1966). Asymptotic properties of some estimators of quantiles of circular error. Journal of the American Statistical Association, 61 (315), 618-632. http://www.jstor.org/stable/2282775
Chew_Boyce_1962
Chew, V., & Boyce, R. (1962). Distribution of radial error in bivariate elliptical normal distributions. Technometrics, 4 (1), 138–140. http://www.jstor.org/stable/1266181
Culpepper_1978
Culpepper, G. A. (1978). Statistical analysis of radial error in two dimensions (Tech. Rep.). White Sands Missile Range, NM
U.S. Army Material Test and Evaluation Directorate. http://handle.dtic.mil/100.2/ADA059117