Goodwin, Roger L
(2014):
*Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.0.*

Preview |
PDF
MPRA_paper_64391.pdf Download (10MB) | Preview |

## Abstract

This book is a practical reference guide accompanied with an Excel Workbook. This book gives an elementary introduction of the weighted standard deviational ellipse. This book also presents the computational aspects of the weighted exponential distributions as well. For the examples given, calculations are performed using VBA for Excel. This book makes comparisons (and shows the computations via VBA for Excel) using the likelihood functions with spatial data of the weighted ellipses. Lastly, the book covers spherical statistics. Throughout the text, the reader can see how to perform these difficult calculations and learn to adapt the code for his research.

Item Type: | MPRA Paper |
---|---|

Original Title: | Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.0 |

English Title: | Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.0 |

Language: | English |

Keywords: | spatial, remote sensing, longitudinal data, statistics, weibull distribution, roger goodwin, roger l goodwin, goodwin, roger l. goodwin exponential distribution, weighted data, map point, google earth, weighted regression, ellipse, area, random variables, spherical statistics, VBA for Excel, mean center, eccentricity, axis length, rotation, weighted mean center, mean latitude, mean longitude, distribution fitting, spherical variance, eigenvalue, eigenvector |

Subjects: | C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics |

Item ID: | 64391 |

Depositing User: | Mr. Roger L Goodwin |

Date Deposited: | 17 May 2015 04:51 |

Last Modified: | 23 May 2023 07:31 |

References: | [1] R. Beran, "Exponential Models for Directional Data," The Annals of Statistics, vol. 7, no. 6 (Nov., 1979), p. 1162-1178. [2] B. L. Bowerman and R. T. O'Connell, Linear Statistical Models, an Applied Approach, Duxbury Press, 1990. [3] G. Brassard and P. Bratley (1988), Algorithmics: Theory and Practice, Prentice Hall, NJ. [4] M. B. Brown and A. B. Forsythe (1974), "Robust Tests for the Equality of Variances," Journal of the American Statistical Association, vol. 69, no. 346, p. 364-367. [5] W. Cheney and D. Kincaid (1985), Numerical Mathematics and Computing, Wadsworth, Inc., Belmont, California. [6] R. S. Chhikara and L. Deng, "Using Multiyear Rotation Design Sampling in Agricultural Surveys," Journal of the American Statistical Association, rm Vol. 87, No. 420 (Dec., 1992), pp. 924-932. [7] L. Cobb, P. Keppstein, and N. H. Chen, "Estimation and Moment Recursion Relations for Multimodal Distributions of the Exponential Family," Journal of the American Statistical Association, rm Vol 78, No. 381 (Mar., 1983), pp. 124-130. [8] W. J. Conover (1999), Practicing Non-Parametric Statistics, Third Edition John Wiley & Sons, Inc., New York, New York. [9] B. R. Crain, "Estimation of Distributions Using Orthogonal Expansions," The Annals of Statistics, vol. 2, no. 3 (May, 1974), p. 454-463. [10] B. R. Crain, "More on Estimation of Distributions Using Orthogonal Expansions," Journal of the American Statistical Association, vol. 71, no. 355 (Sep., 1976), p. 741-745. [11] N. Cressie, Statistics for Spatial Data (Revised Edition), John Wiley & Sons, Inc., New York, 1993. [12] P. Davis, Data Description and Presentation, Oxford University Press, Ely House, London, 1974. [13] D. Ebdon (1985), Statistics in Geography, Second Edition, rm Basil Blackwell, New York, NY. [14] J. Fagan, "Generating Implied Ratio Edits," upublished Census manuscript. October 1999. [15] G. D. Faulkenberry and A. Garoui, "Estimating a Population Total Using an Area Frame," Journal of the American Statistical Association, rm Vol. 86, No. 414 (Jun., 1991), pp. 445-449. [16] I. P. Fellegi and D. Holt, "A Systematic Approach to Automatic Edit and Imputation," The Journal of the American Statistical Association, No. 71, 1976. [17] L. M. Friedman, C. D. Furberg and D. L. DeMets (1996), Fundamentals of Clinical Trials, Third Edition, Mosby-Year Book, Inc., St. Louis, Missouri. [18] J. Gong, "Clarifying the Standard Deviational Ellipse," Geographical Analysis, Vol. 34, No. 2 (April 2002), pp. 155-167. [19] M. Garcia and R. Goodwin, "Developing SAS Software for Generating a Complete Set of Ratio Edits," Statistical Research Division, US Census Bureau, Research Report Series, Statistics # 2002-06, November 8, 2002. [20] R. Goodwin, M. Garcia and K. Thompson, "The GenBounds Software for Generating a Complete Set of Ratio Edits:%Implied User's Guide," Statistical Research Division Report SS-Statistics # 2002-01. [21] B. Greenberg and T. Petkunas, "SPEER (Structured Program for Economic Editing and Referrals)," Proceedings of the Section on Survey Research Methods, American Statistical Association, 1990. [22] S. Gregory, Statistical Methods and the Geographer, Second Edition, Longmans, Green, and Co. Ltd, London and Harlow, 1969. [23] S. I. Grossman (1984), Elementary Linear Algebra, Wadsworth Publishing Company, Belmont, California. [24] J. Hajek and Z. Sidak (1967), Theory of Rank Tests, Academic Press, New York, New York. [25] J. Hajek, Z. Sidak and P. K. Sen (1999), Theory of Rank Tests, Academic Press, San Diego, California. [26] Hammond, Student Notebook Atlas, Hammond World Atlas Corporation, 2010. [27] F. S. Hillier and G. J. Lieberman (1990), Introduction to Operations Research, McGraw-Hill Publishing Company, New York, New York. [28] R. V. Hogg and A. T. Craig (1995), Introduction to Mathematical Statistics, Fifth Edition Prentice Hall, Upper Saddle River, New Jersey. [29] R. V. Hogg and E. A. Tanis (1993), Probability and Statistical Inference, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. [30] M. Hollander and D. A. Wolfe (1999), Nonparametric Statistical Methods, Second Edition, John Wiley & Sons, Inc., New York, New York. [31] R. J. Johnston, Multivariate Statistical Analysis in Geography, Longman Group Limited, Longman, Inc., New York, 1978. [32] B. W. Kelly, "Probability Sampling in Collecting Farm Data," Journal of Farm Economics, Vol. 45, No. 5, Dec. 1963, pp. 1515-1520. [33] R. Khattree and D. N. Naik, Applied Multivariate Statistics with SAS Software, SAS Institute, Inc., Cary, North Carolina, 1995. [34] A. R. Kokan and S. Khan, "Optimum Allocation in Multivariate Surveys: An Analytical Solution," Journal of the Royal Statistical Society, Series B (Methodological), Vol. 29, No. 1, 1967, pp. 115-125. [35] E.T. Lee, Statistical Methods for Survival Data Analysis, Second Edition, John Wiley & Sons, Inc., New York, 1992. [36] J. Lee and D. W. S. Wong, Statistical Analysis with Arc View GIS, John Wiley & Sons, Inc., New York, 2001. [37] E. L. Lehmann and H. J. M. D'Abrera (1975), Nonparametrics, Statistical Methods Based on Ranks, Holden-Day, Inc., Oakland, California. [38] P. Leong and S. Carlile, "Methods for Spherical Data Analysis and Visualization," Journal of Neuroscience Methods, vol. 80, 1998, pp. 191–200. labelleong [39] P. A. W. Lewis (1966), "A Computer Program for the Statistical Analysis of Series of Events," IBM Systems Journal, vol. 5, no. 4. [40] D. W. Lefever, "Measuring Geographic Concentration by Means of the Standard Deviational Ellipse," The American Journal of Sociology, Vol. 32, No. 1. Jul., 1926, pp. 88-94. [41] R. V. Lenth, "Some Practical Guidelines for Effective Sample Size Determination," The American Statistician, rm Vol. 55, No. 3 (Aug., 2001), pp. 187-193. [42] L. Magee, "Improving Survey-Weighted Least Squares Regression," Journal of the Royal Statistical Society, Series B (Statistical Methodology), Blackwell Publishing for the Royal Statistical Society, Vol. 60, No. 1, 1998, pp 115-126. [43] K. V. Mardia, "Statistics of Directional Data," Journal of the Royal Statistical Society, Series B (Methodological), Vol. 37, No. 3 (1975), p. 349-393. [44] K. V. Mardia, Statistics of Directional Data, rm Academic Press, New York, New York, 1972, pp. 52-58. labelmardia [45] K. V. Mardia and P. E. Jupp, Directional Statistics, rm John Wiley & Sons, West Susses, England, 2000. [46] A. Matei and Y. Tille, "Maximal and Minimal Sample Co-Ordination," Sankhya: The Indian Journal of Statistics (2003), rm Vol. 67, No. 3 (Aug., 2005), pp. 590-612. [47] A. M. Mood (1954), "On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests," The Annals of Mathematical Statistics, vol. 25, no. 3, p. 514-522. labelmood [48] L. E. Moses (1963), "Rank Tests for Dispersion," The Annals of Mathematical Statistics, vol 34, no. 3, , p. 973-983. [49] R. G. Petersen, Design and Analysis of Experiments Marcel Dekker, Inc., New York, New York, 1985. [50] P. W. Porter, "What is the Point of Minimum Aggregate Travel?," Annals of the Association of American Geographers, Vol. 53, No. 2, Taylor & Francis, Ltd. on behalf of the Association of American Geographers, Jun., 1963, pp. 224-232. [51] N. D. Pratt, A. C. Bird, J. C. Taylor, and R. C. Carter, "Estimating Areas of Land Under Small-Scale Irrigation Using Satellite Imagery and Ground Data for a Study in N.E. Nigeria," The Geographical Journal, rm Vol. 163, No. 1(Mar., 1997), pp. 65-77. [52] M. L. Puri (1964), "Asymptotic Efficiency of a Class of $c-$sample Tests," The Annals of Mathematical Statistics, vol 35, no. 1, p. 102 - 121. [53] V. F. Rickey and P. M. Tuchinsky, "An Application of Geography to Mathematics: History of the Integral of the Secant," Mathematics Magazine, rm Vol. 53, No. 3 (May, 1980), pp. 162-166. [54] D. B. Rubin, "Composite Points in Weighted Least Squares Regressions," Technometrics, Vol. 22, No. 3, Aug. 1980, pp. 343-348. [55] C. E. Sarndal, B. Swensson and J. Wretman (1999), Model Assisted Survey Sampling, Springer-Verlag New York, Inc., New York, New York. [56] B. Shelby, "Girdle Distributions on the Sphere," Biometrika Trust, Vol. 51, No. 3/4, Dec. 1964, pp. 381-392. [57] F. Solomon (1987), Probability and Stochastic Processes, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. [58] D. J. Steffensmeier, E. A. Allan, M. D. Harer and C. Streifel, "Age and the Distribution of Crime," The American Jouranl of Sociology, rm Vol. 94, No. 4 (Jan., 1989), pp. 803-831. [59] K. J. Thompson and R. Sigman, "Statistical Methods for Developing Ratio Edit Tolerances for Economic Data," Journal of Official Statistics, 2000. [60] G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, Fifth Edition, Addison-Wesley Publishing Company, Reading Massachusetts, 1979. [61] W. Winkler and L. Draper, "The SPEER Edit System," Proceedings of the Conference of European Statisticians, Section on Statisticial Editing, UNECE, 1997. [62] C. A. Wolf and D. A. Sumner, "Are Farm Size Distributions Bimodal? Evidence from Kernel Density Estimates of Dairy FarmSize Distributions," American Journal of Agricultural Economics, vol. 83, no. 1 (Feb., 2001), p. 77-88. [63] A. Wood, "A Bimodal Distribution on the Sphere," Journal of the Royal Statistical Society. Series C (Applied Statistics), rm Vol. 31, No. 1 (1982), pp. 52-58. [64] R. F. Woolson and W. R. Clarke, "Analysis of Categorical Incomplete Longitudinal Data," Journal of the Royal Statistical Society, Series A (General), Blackwell Publishing for the Royal Statistical Society, Vol. 147, No. 1, 1984, pp 87-99. [65] J. Yu, Z. Yang and X. Zhang (2002), "A Class of Nonlinear Stochastic Volatility Models and its Implications on Pricing Currency Options," www.buseco. monash.edu.au/ depts/ebs/pubs/ wpapers/2002/wp17-02.pdf. [66] R. S. Yuill, "The Standard Deviational Ellipse: An Updated Tool for Spatial Description," Geografisker Annaler, Series B, Human Geography, Vol 53, No. 1, Blackwell Publishing on behalf of the Swedish Society for Anthropology and Geography, 1971, pp. 28-39. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/64391 |