Probability and statistics

This chapter introduces the calculating techniques of probability and statistics as well as their applications in geosciences. For each technique, the applying ranges and conditions, basic principles, calculation methods, and case studies are provided. Each case study contains the relevant calculation flowchart, calculation results, and analyses. Though each case study is small, it reflects the whole process of calculations to benefit readers in understanding and mastering the techniques applied. Though some flowcharts are drawn for specific case studies, they are actually all-purpose only if the specific case study is replaced by readers’ own application samples.

[1]  On the Coincidence Property of Stochastic Matrices , 1983 .

[2]  P. Hsu,et al.  On the Limiting Distribution of Roots of a Determinantal Equation , 1941 .

[3]  P. Hsu.  ANALYSIS OF VARIANCE FROM THE POWER FUNCTION STANDPOINT , 1941 .

[4]  P. Hsu.  On the Approximate Distribution of Ratios , 1945 .

[5]  A new proof of the joint product moment distribution , 1939 .

[6]  T. Kiang,et al.  A Note on the Indices and Numbers of Nondegenerate Critical Points of Biharmonic Functions , 1983 .

[7]  Xin-She Yang,et al.  Optimization and data mining for fracture prediction in geosciences , 2010, ICCS.

[8]  H NAGLER,et al.  On the best unbiased quadratic estimate of the variance. , 1950, Biometrika.

[9]  P. Hsu.  The Approximate Distributions of the Mean and Variance of a Sample of Independent Variables , 1945 .

[10]  S. Chatterjee,et al.  Regression Analysis by Example , 1979 .

[11]  ON A FACTORIZATION OF PSEUDO-ORTHOGONAL MATRICES , 1946 .

[12]  Guang-Ren Shi,et al.  The use of support vector machine for oil and gas identification in low-porosity and low-permeability reservoirs , 2009, Int. J. Math. Model. Numer. Optimisation.

[13]  P. Hsu.  ON THE DISTRIBUTION OF ROOTS OF CERTAIN DETERMINANTAL EQUATIONS , 1939 .

[14]  P. Hsu,et al.  ON THE PROBLEM OF RANK AND THE LIMITING DISTRIBUTION OF FISHER'S TEST FUNCTION , 1941 .

[15]  P. Hsu,et al.  ON THE LIMITING DISTRIBUTION OF THE CANONICAL CORRELATIONS , 1941 .

[16]  P. Hsu.  On the Power Functions of the $E^2$-Test and the $T^2$-Test , 1945 .

[17]  Seung-Han Yang,et al.  Statistical optimization and assessment of a thermal error model for CNC machine tools , 2002 .

[18]  P. Hsu.  CANONICAL REDUCTION OF THE GENERAL REGRESSION PROBLEM , 1941 .

[19]  P. Hsu.  ON GENERALIZED ANALYSIS OF VARIANCE. (I) , 1940 .

[20]  Tuanfeng Zhang.  Numerical Methods of Petroliferous Basin Modeling , 2006 .

[21]  H Robbins,et al.  Complete Convergence and the Law of Large Numbers. , 1947, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Guangren Shi,et al.  Four Classifiers Used in Data Mining and Knowledge Discovery for Petroleum Exploration and Development , 2011 .

[23]  P. Hsu.  An algebraic derivation of the distribution of rectangular coordinates , 1940 .

[24]  P. Khadikar,et al.  Comparative QSAR Study on Para‐substituted Aromatic Sulphonamides as CAII Inhibitors: Information versus Topological (Distance‐Based and Connectivity) Indices , 2008, Chemical biology & drug design.

[25]  P. Hsu,et al.  Notes on Hotelling's Generalized $T$ , 1938 .

[26]  P. Hsu.  On the Asymptotic Distributions of Certain Statistics Used in Testing the Independence Between Successive Observations from a Normal Population , 1946 .

[27]  P. Hsu.  On Symmetric, Orthogonal, and Skew-Symmetric Matrices , 1953 .

[28]  G. Shi,et al.  The use of artificial neural network analysis and multiple regression for trap quality evaluation: a case study of the Northern Kuqa Depression of Tarim Basin in western China , 2004 .

[29]  Kai Lai Chung.  Absolute Moments and Characteristic Function , 1983 .