Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions Page: iv
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Contents
ACKNOWLEDGEMENTS iii
1 Introduction 1
2 Background 3
2.1 The Sequential Barycenter Array Construction . . . . . . . . . . . . 3
2.2 Approximations Of SBA Random Probability Measure Constructions 10
2.3 The Distribution Of Moments In The Support Of B, 1........... 23
3 Random Splittings Of An Interval 37
3.1 A Splitting Model....... ...................... ..... 37
3.2 Numerical Methods . ........................... 46
3.2.1 An Algorithm For Approximating F . . . . . . . . . . ... 46
4 Simulations Of Statistics For SBA Constructions 53
4.1 Introduction And Simulation Implementation . . . . . . . . . . .. 53
4.2 The Second Moment .. .......................... 58
4.3 The Standard Deviation ......................... 68
4.4 The Third Moment . ........................... 76
4.5 The Third Central Moment and Skewness . . . . . . . . . . ..... 84
4.6 The Fourth Moment ...... .......................... 95
4.7 The Fourth Central Moment and Kurtosis .................. 103
4.8 Conclusions And Open Questions ...... ................. 115iv
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Valdes, LeRoy I. Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions, dissertation, December 2002; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc3304/m1/6/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .