TAILIEUCHUNG - Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 134

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 134', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Two-Dimensional Distributions Differ 645 li l j decoding its row lj l-j li and column. mm m1 li-ki m2 lj-kj pairs tab ki 1 kj 1 tab li 1 lj 1 if mm Not a tie. en1 pairs en2 pairs s mm 0 pairs -pairs Concordant or discordant. else if m1 en1 pairs if m2 en2 pairs tau s sqrt en1 en2 svar points points z tau sqrt svar prob erfcc fabs z CITED REFERENCES AND FURTHER READING Lehmann . 1975 Nonparametrics Statistical Methods Based on Ranks San Francisco Holden-Day . Downie . and Heath . 1965 Basic Statistical Methods 2nd ed. New York Harper Row pp. 206-209. Norusis SPSS Introductory Guide Basic Statistics and Operations and 1985 SPSS-XAdvanced Statistics Guide New York McGraw-Hill . Do Two-Dimensional Distributions Differ We here discuss a useful generalization of the K-S test to two-dimensional distributions. This generalization is due to Fasano and Franceschini 1 a variant on an earlier idea due to Peacock 2 . In a two-dimensional distribution each data point is characterized by an x y pair of values. An example near to our hearts is that each of the 19 neutrinos that were detected from Supernova 1987A is characterized by a time ti and by an energy Ei see 3 . We might wish to know whether these measured pairs ti Ei i 1. 19 are consistent with a theoretical model that predicts neutrino flux as a function of both time and energy that is a two-dimensional probability distribution in the x y here t E plane. That would be a one-sample test. Or given two sets of neutrino detections from two comparable detectors we might want to know whether they are compatible with each other a two-sample test. In the spirit of the tried-and-true one-dimensional K-S test we want to range over the x y plane in search of some kind of maximum cumulative difference between two two-dimensional distributions. Unfortunately cumulative probability distribution is not well-defined in more than one dimension Peacock s insight was that

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