Transformation of a normal statistical variate, with applications to curve-fitting

Abstract

CHAPTER I: Transformation of Statistical Variate: 1.1 The two approaches to the problem of skewness; 1.2 Transformation of statistical variate; 1.3 Macalister's curve for geometric mean; 1.4 Edgeworth's method of translation; 1.5 Kapteyn's theory and curves; 16 A basis for Kapteyn's general curve in symbolic generating functions for non-additive variates; 1.7 Conclusion.CHAPTER II: Polynomial transformation of normal variate: 2.1 Polynomial transformation of normal variate; 2.2 Fitting by moments; 2.3 Fitting by quantiles; 2.4 Prof. Aitken's solution of a set of inconsistent linear equations; 2.5 Prof. Aitken's method of fitting polynomials to correlated data; 2.6 The Reciprocal of the variance matrix for quantiles; 2.7 Standard matrices for W and solutions; 2.8 Variances of solutions; 2.9 Changes in Standard Results for negative skewness; 2.10 Fitting the transformation to the data; 2.11 Method of finding the quartiles; 2.12 An alternative basis for standardizing W matrices.CHAPTER III: Exponential transformation of normal variate: 3.1 Exponential transformation of normal variate; 3.2 Macalister's curve: Estimation of the parameters and properties: 3.3 The general case.CHAPTER IV Numerical Examples: 4.1 Distribution of weights of 7749 Adults born in U.K.; 4.2 Distribution of weights of 11382 Glasgow school children.APPENDIX I Normal Sextiles and Octiles with their powers; APPENDIX II Abscissae and Ordinates at Sextiles and Octiles of Pearson's Type III curve; APPENDIX III Standard Results for Sextiles and Octiles from level of skewness 0.1 to 1.1; APPENDIX IV Variances of Solutions; APPENDIX V Details of computation of Standard Results for Octiles, level of skew .=0.5; APPENDIX VI A note on the distribution of n-iles in large samples; References.