Difference between revisions of "CEP literature"

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* <div id="Blischke1966"></div>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
 
* <div id="Blischke1966"></div>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
 
* <div id="Chew1962"></div>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
 
* <div id="Chew1962"></div>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
−
* <div id="DiDonato2004"></div>DiDonato, A. (2004). An inverse of the generalized circular error function (Tech. Rep. No. NSWCDD/TR-04/43). Dahlgren, VA: Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA476368
+
* <div id="Culpepper1978"></div>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
−
* <div id="DiDonato2007"></div>DiDonato, A. (2007). Computation of the Circular Error Probable (CEP) and Confidence Intervals in Bombing Tests (Tech. Rep. No. NSWCDD/TR-07/13). Dahlgren, VA: Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA476368
+
* <div id="DiDonato1988"></div>DiDonato, A. R. (1988). Integration of the trivariate normal distribution over an offset spehere and an inverse problem (Tech. Rep. No. NSWC TR 87-27). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://www.dtic.mil/dtic/tr/fulltext/u2/a198129.pdf
−
* <div id="Elder1986"></div>Elder, R. L. (1986). An examination of circular error probable approximation techniques (Tech. Rep. No. AFIT/GST/ENS/86M-6). Wright-Patterson AFB, OH: Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA172498
+
* <div id="DiDonato2004"></div>DiDonato, A. (2004). An inverse of the generalized circular error function (Tech. Rep. No. NSWCDD/TR-04/43). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA476368
−
* <div id="Ethridge1983"></div>Ethridge, R. A. (1983). Robust estimation of circular error probable for small samples (Tech. Rep. No. ACSC 83-0690). Maxwell AFB, AL: Air Command and Staff College.
+
* <div id="DiDonato2007"></div>DiDonato, A. (2007). Computation of the Circular Error Probable (CEP) and Confidence Intervals in Bombing Tests (Tech. Rep. No. NSWCDD/TR-07/13). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA476368
−
* <div id="Greenwalt1962"></div>Greenwalt, C. R., & Shultz, M. E. (1962). Principles of Error Theory and Cartographic Applications (Tech. Rep. No. ACIC TR-96). St. Louis, MO: Aeronautical Chart & Information Center. http://earth-info.nga.mil/GandG/publications/tr96.pdf
+
* <div id="DiDonato1961a"></div>DiDonato, A. R., & Jarnagin, M. P. (1961a). Integration of the general bivariate Gaussian distribution over an offset circle. Mathematics of Computation, 15 (76), 375–382. http://www.jstor.org/stable/2003026
 +
* <div id="DiDonato1961b"></div>DiDonato, A. R., & Jarnagin, M. P. (1961b). Integration of the general bivariate Gaussian distribution over an offset ellipse (Tech. Rep. No. NWL TR 1710). Dahlgren, VA: U.S. Naval Weapons Laboratory.
 +
* <div id="DiDonato1962a"></div>DiDonato, A. R., & Jarnagin, M. P. (1962a). A method for computing the circular coverage function. Mathematics of Computation, 16 (79), 347–355. http://www.jstor.org/stable/2004054
 +
* <div id="DiDonato1962b"></div>DiDonato, A. R., & Jarnagin, M. P. (1962b). A method for computing the generalized circular error function and the circular coverage function (Tech. Rep. No. NWL TR 1786). Dahlgren, VA: U.S. Naval Weapons Laboratory.
 +
* <div id="Duchesne2010"></div>Duchesne, P., & Lafaye de Micheaux, P. (2010). Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods. Computational Statistics and Data Analysis, 54 (4), 858–862.
 +
* <div id="Elder1986"></div>Elder, R. L. (1986). An examination of circular error probable approximation techniques (Tech. Rep. No. AFIT/GST/ENS/86M-6). Wright-Patterson AFB, OH: U.S. Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA172498
 +
* <div id="Ethridge1983"></div>Ethridge, R. A. (1983). Robust estimation of circular error probable for small samples (Tech. Rep. No. ACSC 83-0690). Maxwell AFB, AL: U.S. Air Command and Staff College.
 +
* <div id="Evans1985"></div>Evans, M. J., Govindarajulu, Z., & Barthoulot, J. (1985). Estimates of circular error probabilities (Tech. Rep. No. TR 367). Arlington, VA: U.S. Office of Naval Research. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA163257
 +
* <div id="Greenwalt1962"></div>Greenwalt, C. R., & Shultz, M. E. (1962). Principles of Error Theory and Cartographic Applications (Tech. Rep. No. ACIC TR-96). St. Louis, MO: U.S. Aeronautical Chart & Information Center. http://earth-info.nga.mil/GandG/publications/tr96.pdf
 
* <div id="Grubbs1944"></div>Grubbs, F. E. (1944). On the distribution of the radial standard deviation. Annals of Mathematical Statistics, 15 (1), 75–81. https://projecteuclid.org/euclid.aoms/1177731316
 
* <div id="Grubbs1944"></div>Grubbs, F. E. (1944). On the distribution of the radial standard deviation. Annals of Mathematical Statistics, 15 (1), 75–81. https://projecteuclid.org/euclid.aoms/1177731316
 
* <div id="Grubbs1964"></div>Grubbs, F. E. (1964). Approximate circular and noncircular offset probabilities of hitting. Operations Research, 12 (1), 51–62. http://www.jstor.org/stable/167752
 
* <div id="Grubbs1964"></div>Grubbs, F. E. (1964). Approximate circular and noncircular offset probabilities of hitting. Operations Research, 12 (1), 51–62. http://www.jstor.org/stable/167752
 
* <div id="Harter1960"></div>Harter, H. L. (1960). Circular error probabilities. Journal of the American Statistical Association, 55 (292), 723–731. http://www.jstor.org/stable/2281595
 
* <div id="Harter1960"></div>Harter, H. L. (1960). Circular error probabilities. Journal of the American Statistical Association, 55 (292), 723–731. http://www.jstor.org/stable/2281595
 
* <div id="Hogg1967"></div>Hogg, R. V. (1967). Some observations on robust estimation. Journal of the American Statistical Association, 62 (320), 1179–1186. http://www.jstor.org/stable/2283768
 
* <div id="Hogg1967"></div>Hogg, R. V. (1967). Some observations on robust estimation. Journal of the American Statistical Association, 62 (320), 1179–1186. http://www.jstor.org/stable/2283768
−
* <div id="Hoover1984"></div>Hoover, W. E. (1984). Algorithms for confidence circles, and ellipses (Tech. Rep. No. NOAA TR NOS 107 C&GS 3). Rockville, MD: National Oceanic and Atmospheric Administration. http://www.ngs.noaa.gov/PUBS_LIB/Brunswick/NOAATRNOS107CGS3.pdf
+
* <div id="Hoover1984"></div>Hoover, W. E. (1984). Algorithms for confidence circles, and ellipses (Tech. Rep. No. NOAA TR NOS 107 C&GS 3). Rockville, MD: U.S. National Oceanic and Atmospheric Administration. http://www.ngs.noaa.gov/PUBS_LIB/Brunswick/NOAATRNOS107CGS3.pdf
 
* <div id="Hoyt1947"></div>Hoyt, R. S. (1947). Probability functions for the modulus and angle of the normal complex variate. Bell System Technical Journal, 26 (2), 318–359. http://www3.alcatel-lucent.com/bstj/vol26-1947/articles/bstj26-2-318.pdf
 
* <div id="Hoyt1947"></div>Hoyt, R. S. (1947). Probability functions for the modulus and angle of the normal complex variate. Bell System Technical Journal, 26 (2), 318–359. http://www3.alcatel-lucent.com/bstj/vol26-1947/articles/bstj26-2-318.pdf
 +
* <div id="Imhof1961"></div>Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 48 (3–4), 419–426. http://www.jstor.org/stable/2332763
 
* <div id="Kamat1962"></div>Kamat, A. R. (1962). Some more estimates of circular probable error. Journal of the American Statistical Association, 57 (297), 191–195. http://www.jstor.org/stable/2282450
 
* <div id="Kamat1962"></div>Kamat, A. R. (1962). Some more estimates of circular probable error. Journal of the American Statistical Association, 57 (297), 191–195. http://www.jstor.org/stable/2282450
 
* <div id="McMillan2008"></div>McMillan, C., & McMillan, P. (2008). Characterizing rifle performance using circular error probable measured via a flatbed scanner. http://statshooting.com/
 
* <div id="McMillan2008"></div>McMillan, C., & McMillan, P. (2008). Characterizing rifle performance using circular error probable measured via a flatbed scanner. http://statshooting.com/
 
* <div id="Moranda1959"></div>Moranda, P. B. (1959). Comparison of estimates of circular probable error. Journal of the American Statistical Association, 54 (288), 794–780. http://www.jstor.org/stable/2282503
 
* <div id="Moranda1959"></div>Moranda, P. B. (1959). Comparison of estimates of circular probable error. Journal of the American Statistical Association, 54 (288), 794–780. http://www.jstor.org/stable/2282503
 
* <div id="Moranda1960"></div>Moranda, P. B. (1960). Effect of bias on estimates of the circular probable error. Journal of the American Statistical Association, 55 (292), 732–735. http://www.jstor.org/stable/2281596
 
* <div id="Moranda1960"></div>Moranda, P. B. (1960). Effect of bias on estimates of the circular probable error. Journal of the American Statistical Association, 55 (292), 732–735. http://www.jstor.org/stable/2281596
 +
* <div id="Nelson1988"></div>Nelson, W. (1988). Use of circular error probability in target detection (Tech. Rep. Nos. ESD-TR-88-109, MTR-10293). Bedford, MA: MITRE Corporation. http://handle.dtic.mil/100.2/ADA199190
 
* <div id="Nuttall1975"></div>Nuttall, A. H. (1975). Some integrals involving the Q-M function. IEEE Transactions on Information Theory, 21 (1), 95-96.
 
* <div id="Nuttall1975"></div>Nuttall, A. H. (1975). Some integrals involving the Q-M function. IEEE Transactions on Information Theory, 21 (1), 95-96.
 
* <div id="Paris2009"></div>Paris, J. F. (2009). Nakagami-q (Hoyt) distribution function with applications. Electronics Letters, 45 (4), 210–211. Erratum: http://dx.doi.org/10.1049/el.2009.0828
 
* <div id="Paris2009"></div>Paris, J. F. (2009). Nakagami-q (Hoyt) distribution function with applications. Electronics Letters, 45 (4), 210–211. Erratum: http://dx.doi.org/10.1049/el.2009.0828
 +
* <div id="Patnaik1949"></div>Patnaik, P. B. (1949). The non-central <math>\chi^{2}</math>- and F-distributions and their applications. Biometrika, 36 (1–2), 202–232. http://www.jstor.org/stable/2332542
 +
* <div id="Pearson1959"></div>Pearson, E. S. (1959). Note on an approximation to the distribution of non-central <math>\chi^{2}</math>. Biometrika, 46 (3–4), 364. http://www.jstor.org/stable/2333533
 
* <div id="Pesapane1977"></div>Pesapane, J., & Irvine, R. B. (1977). Derivation of CEP formula to approximate RAND-234 tables (Tech. Rep.). Offut AFB, NE: Ballistic Missile Evaluation, HQ SAC.
 
* <div id="Pesapane1977"></div>Pesapane, J., & Irvine, R. B. (1977). Derivation of CEP formula to approximate RAND-234 tables (Tech. Rep.). Offut AFB, NE: Ballistic Missile Evaluation, HQ SAC.
−
* <div id="Puhek1992"></div>Puhek, P. (1992). Sensitivity analysis of circular error probable approximation techniques (Tech. Rep. No. AFIT/GOR/ENS/92M-23). Wright-Patterson AFB, OH: Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA248105
+
* <div id="Puhek1992"></div>Puhek, P. (1992). Sensitivity analysis of circular error probable approximation techniques (Tech. Rep. No. AFIT/GOR/ENS/92M-23). Wright-Patterson AFB, OH: U.S. Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA248105
 
* <div id="Pyati1993"></div>Pyati, V. P. (1993). Computation of the circular error probability (CEP) integral. IEEE Transactions on Aerospace and Electronic Systems, 29 (3), 1023–1024.
 
* <div id="Pyati1993"></div>Pyati, V. P. (1993). Computation of the circular error probability (CEP) integral. IEEE Transactions on Aerospace and Electronic Systems, 29 (3), 1023–1024.
 
* <div id="RAND1952"></div>RAND Corporation. (1952). Offset circle probabilities (Tech. Rep. No. RAND-234). Santa Monica, CA: RAND Corporation. http://www.rand.org/pubs/reports/2008/R234.pdf
 
* <div id="RAND1952"></div>RAND Corporation. (1952). Offset circle probabilities (Tech. Rep. No. RAND-234). Santa Monica, CA: RAND Corporation. http://www.rand.org/pubs/reports/2008/R234.pdf
−
* <div id="Sathe1991"></div>Sathe, Y. S., Joshi, S. M., & Nabar, S. P. (1991). Bounds for circular error probabilities. Naval Research Logistics (NRL), 38 (1), 33–40.
+
* <div id="Sathe1991"></div>Sathe, Y. S., Joshi, S. M., & Nabar, S. P. (1991). Bounds for circular error probabilities. U.S. Naval Research Logistics (NRL), 38 (1), 33–40.
 +
* <div id="Saxena2005"></div>Saxena, S., & Singh, H. P. (2005). Some estimators of the dispersion parameter of a chi-distributed radial error with applications to target analysis. Austrial Journal of Statistics, 34 (1), 51–63. http://www.stat.tugraz.at/AJS/ausg051/051Saxena&Singh.pdf
 
* <div id="Shnidman1995"></div>Shnidman, D. A. (1995). Efficient computation of the circular error probability (CEP) integral. IEEE Transactions on Automatic Control, 40 (8), 1472–1474.
 
* <div id="Shnidman1995"></div>Shnidman, D. A. (1995). Efficient computation of the circular error probability (CEP) integral. IEEE Transactions on Automatic Control, 40 (8), 1472–1474.
 
* <div id="Singh1992"></div>Singh, H. P. (1992). Estimation of Circular Probable Error. The Indian Journal of Statistics, Series B, 54 (3), 289–305. http://www.jstor.org/stable/25052751
 
* <div id="Singh1992"></div>Singh, H. P. (1992). Estimation of Circular Probable Error. The Indian Journal of Statistics, Series B, 54 (3), 289–305. http://www.jstor.org/stable/25052751
−
* <div id="Taub1983a"></div>Taub, A. E., & Thomas, M. A. (1983a). Comparison of CEP estimators for elliptical normal errors (Tech. Rep. No. ADP001580). Dahlgren, VA: Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA153828
+
* <div id="Singh1962"></div>Singh, N. (1962). Spherical probable error. Nature, 193 (4815), 605. http://www.nature.com/nature/journal/v193/n4815/abs/193605a0.html
−
* <div id="Taub1983b"></div>Taub, A. E., & Thomas, M. A. (1983b). Confidence Intervals for CEP When the Errors are Elliptical Normal (Tech. Rep. No. NSWC/TR-83-205). Dahlgren, VA: Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA153828
+
* <div id="Singh1970"></div>Singh, N. (1970). Spherical probable error (SPE) and its stimation. Metrika, 15 (1), 149–163.
−
* <div id="Tongue1993"></div>Tongue, W. L. (1993). An empirical evaluation of five circular error probable estimation techniques and a method for improving them (Tech. Rep. No. AFIT/GST/ENS/93M-13). Wright-Patterson AFB, OH: Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA266528
+
* <div id="Taub1983a"></div>Taub, A. E., & Thomas, M. A. (1983a). Comparison of CEP estimators for elliptical normal errors (Tech. Rep. No. ADP001580). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA153828
 +
* <div id="Taub1983b"></div>Taub, A. E., & Thomas, M. A. (1983b). Confidence Intervals for CEP When the Errors are Elliptical Normal (Tech. Rep. No. NSWC/TR-83-205). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA153828
 +
* <div id="Tongue1993"></div>Tongue, W. L. (1993). An empirical evaluation of five circular error probable estimation techniques and a method for improving them (Tech. Rep. No. AFIT/GST/ENS/93M-13). Wright-Patterson AFB, OH: U.S. Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA266528
 
* <div id="Wang2013a"></div>Wang, Y., Jia, X. R., Yang, G., & Wang, Y. M. (2013). Comprehensive CEP evaluation method for calculating positioning precision of navigation systems. Applied Mechanics and Materials, 341–342, 955–960.
 
* <div id="Wang2013a"></div>Wang, Y., Jia, X. R., Yang, G., & Wang, Y. M. (2013). Comprehensive CEP evaluation method for calculating positioning precision of navigation systems. Applied Mechanics and Materials, 341–342, 955–960.
 
* <div id="Wang2013b"></div>Wang, Y., Yang, G., Jia, X. R., & Wang, Y. M. (2013). Comprehensive TCEP assessment of methods for calculating MUAV navigation position accuracy based on visual measurement. Advanced Materials Research, 765–767, 2224–2228.
 
* <div id="Wang2013b"></div>Wang, Y., Yang, G., Jia, X. R., & Wang, Y. M. (2013). Comprehensive TCEP assessment of methods for calculating MUAV navigation position accuracy based on visual measurement. Advanced Materials Research, 765–767, 2224–2228.
 
* <div id="Wang2014"></div>Wang, Y., Yang, G., Yan, D., Wang, Y. M., & Song, X. (2014). Comprehensive assessment algorithm for calculating CEP of positioning accuracy. Measurement, 47 (January), 255–263.
 
* <div id="Wang2014"></div>Wang, Y., Yang, G., Yan, D., Wang, Y. M., & Song, X. (2014). Comprehensive assessment algorithm for calculating CEP of positioning accuracy. Measurement, 47 (January), 255–263.
−
* <div id="Williams1997"></div>Williams, C. E. (1997). A comparison of circular error probable estimators for small samples (Tech. Rep. No. AFIT/GOA/ENS/97M-14). Wright-Patterson AFB, OH: Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA324337
+
* <div id="Williams1997"></div>Williams, C. E. (1997). A comparison of circular error probable estimators for small samples (Tech. Rep. No. AFIT/GOA/ENS/97M-14). Wright-Patterson AFB, OH: U.S. Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA324337
 
* <div id="Zhang2012"></div>Zhang, J., & An, W. (2012). Assessing circular error probable when the errors are elliptical normal. Journal of Statistical Computation and Simulation, 82 (4), 565–586.
 
* <div id="Zhang2012"></div>Zhang, J., & An, W. (2012). Assessing circular error probable when the errors are elliptical normal. Journal of Statistical Computation and Simulation, 82 (4), 565–586.

Revision as of 11:36, 28 February 2014

The literature on the circular error probable (CEP) is extensive and diverse: Applications for CEP are found in areas such as target shooting, missile ballistics, or positional accuracy of navigation and guidance systems like GPS. The statistical foundation also has applications in (wireless) signal processing.

Groups of CEP publications

The following list is by no means intended to be complete. In particular, it contains no references to the 3D-generalization to the spherical error probable (SEP). Beware that the quality of the listed publications is mixed. The relevant publications may be roughly categorized into four groups:

List of references

  • 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, 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, 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
  • DiDonato, A. R. (1988). Integration of the trivariate normal distribution over an offset spehere and an inverse problem (Tech. Rep. No. NSWC TR 87-27). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://www.dtic.mil/dtic/tr/fulltext/u2/a198129.pdf
  • DiDonato, A. (2004). An inverse of the generalized circular error function (Tech. Rep. No. NSWCDD/TR-04/43). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA476368
  • DiDonato, A. (2007). Computation of the Circular Error Probable (CEP) and Confidence Intervals in Bombing Tests (Tech. Rep. No. NSWCDD/TR-07/13). Dahlgren, VA: U.S. Naval Surface Weapons Center Dahlgren Division. http://handle.dtic.mil/100.2/ADA476368
  • DiDonato, A. R., & Jarnagin, M. P. (1961a). Integration of the general bivariate Gaussian distribution over an offset circle. Mathematics of Computation, 15 (76), 375–382. http://www.jstor.org/stable/2003026
  • DiDonato, A. R., & Jarnagin, M. P. (1961b). Integration of the general bivariate Gaussian distribution over an offset ellipse (Tech. Rep. No. NWL TR 1710). Dahlgren, VA: U.S. Naval Weapons Laboratory.
  • DiDonato, A. R., & Jarnagin, M. P. (1962a). A method for computing the circular coverage function. Mathematics of Computation, 16 (79), 347–355. http://www.jstor.org/stable/2004054
  • DiDonato, A. R., & Jarnagin, M. P. (1962b). A method for computing the generalized circular error function and the circular coverage function (Tech. Rep. No. NWL TR 1786). Dahlgren, VA: U.S. Naval Weapons Laboratory.
  • Duchesne, P., & Lafaye de Micheaux, P. (2010). Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods. Computational Statistics and Data Analysis, 54 (4), 858–862.
  • Elder, R. L. (1986). An examination of circular error probable approximation techniques (Tech. Rep. No. AFIT/GST/ENS/86M-6). Wright-Patterson AFB, OH: U.S. Air Force Institute of Technology. http://handle.dtic.mil/100.2/ADA172498
  • Ethridge, R. A. (1983). Robust estimation of circular error probable for small samples (Tech. Rep. No. ACSC 83-0690). Maxwell AFB, AL: U.S. Air Command and Staff College.
  • Evans, M. J., Govindarajulu, Z., & Barthoulot, J. (1985). Estimates of circular error probabilities (Tech. Rep. No. TR 367). Arlington, VA: U.S. Office of Naval Research. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA163257
  • Greenwalt, C. R., & Shultz, M. E. (1962). Principles of Error Theory and Cartographic Applications (Tech. Rep. No. ACIC TR-96). St. Louis, MO: U.S. Aeronautical Chart & Information Center. http://earth-info.nga.mil/GandG/publications/tr96.pdf
  • Grubbs, F. E. (1944). On the distribution of the radial standard deviation. Annals of Mathematical Statistics, 15 (1), 75–81. https://projecteuclid.org/euclid.aoms/1177731316
  • Grubbs, F. E. (1964). Approximate circular and noncircular offset probabilities of hitting. Operations Research, 12 (1), 51–62. http://www.jstor.org/stable/167752
  • Harter, H. L. (1960). Circular error probabilities. Journal of the American Statistical Association, 55 (292), 723–731. http://www.jstor.org/stable/2281595
  • Hogg, R. V. (1967). Some observations on robust estimation. Journal of the American Statistical Association, 62 (320), 1179–1186. http://www.jstor.org/stable/2283768
  • Hoover, W. E. (1984). Algorithms for confidence circles, and ellipses (Tech. Rep. No. NOAA TR NOS 107 C&GS 3). Rockville, MD: U.S. National Oceanic and Atmospheric Administration. http://www.ngs.noaa.gov/PUBS_LIB/Brunswick/NOAATRNOS107CGS3.pdf
  • Hoyt, R. S. (1947). Probability functions for the modulus and angle of the normal complex variate. Bell System Technical Journal, 26 (2), 318–359. http://www3.alcatel-lucent.com/bstj/vol26-1947/articles/bstj26-2-318.pdf
  • Imhof, J. P. (1961). Computing the distribution of quadratic forms in normal variables. Biometrika, 48 (3–4), 419–426. http://www.jstor.org/stable/2332763
  • Kamat, A. R. (1962). Some more estimates of circular probable error. Journal of the American Statistical Association, 57 (297), 191–195. http://www.jstor.org/stable/2282450
  • McMillan, C., & McMillan, P. (2008). Characterizing rifle performance using circular error probable measured via a flatbed scanner. http://statshooting.com/
  • Moranda, P. B. (1959). Comparison of estimates of circular probable error. Journal of the American Statistical Association, 54 (288), 794–780. http://www.jstor.org/stable/2282503
  • Moranda, P. B. (1960). Effect of bias on estimates of the circular probable error. Journal of the American Statistical Association, 55 (292), 732–735. http://www.jstor.org/stable/2281596
  • Nelson, W. (1988). Use of circular error probability in target detection (Tech. Rep. Nos. ESD-TR-88-109, MTR-10293). Bedford, MA: MITRE Corporation. http://handle.dtic.mil/100.2/ADA199190
  • Nuttall, A. H. (1975). Some integrals involving the Q-M function. IEEE Transactions on Information Theory, 21 (1), 95-96.
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