Selecting and Ordering Populations: A New Statistical Methodology

Properties of distance spaces with power triangle inequalities

“…Let ℝ + be the set of all positive real numbers and ℝ * be the set of extended real numbers (Definition 2.1 page 4 [Blumenthal(1953)] pages 12-13, [Laos(1998)] pages 118-119 36 This is the method of "inscribed polygons" for calculating the length of a curve and goes back to Archimedes: [Brunschwig et al(2003) [Sherstnev(1962)], page 4, [Schweizer and Sklar(1983)] page 9 ⟨(1.6.1)-(1.6.4)⟩, [Bessenyei and Pales(2014) [Kirk and Shahzad(2014)] page 113 ⟨Definition 12.1⟩, [Deza and Deza(2014)] page 7, [Hoehn and Niven(1985)] page 151, [Gibbons et al(1977)Gibbons, Olkin, and Sobel] page 51 ⟨square-meanroot (SMR) (2.4.1)⟩, [Euclid(circa 300BC)] ⟨triangle inequality-Book I Proposition 20⟩ 39 metric space: [Dieudonné(1969)], page 28, [Copson(1968)], page 21, [Hausdorff(1937)] page 109, [Fréchet(1928)], [Fréchet(1906)] page 30 near metric space: [Czerwik(1993)] page 5 ⟨b-metric; (1),(2),(5)⟩, [Fagin et al(2003a)Fagin, Kumar, and Sivakumar], [Fagin et al(2003b) …”

The Epistemology of Statistical Science

“…If we consult other sources, the same inappropriate exemplification is found. Gibbons, Olkin and Sobel (1977) for instance, try to complement 'theory' books like that of Gupta and Panchapakesan, with a 'methods' book. So they present many purported examples for decision-making under risk, but again we find that time and again we are presented with an example requiring data analysis, rather than decision-making under risk.…”

Investigation of Genetic Algorithms for Computer-Aided Diagnosis

“…Because, however, the measured A z values have a distribution associated with them, there is a measurable probability that one or more of the "worse" features (those features with a theoretical A z value of A^2 ) < A^) will be selected. Using order statistics [12][13][14][15], we have derived the probability that an optimal subset of features will be selected in the situation described above:…”