Dragons and bulls : profitable investment strategies for trading stocks and commodities

Title Page Preface CONTENTS 1. Introduction - Meaning and Scope 1.1 Origin and Development of Statitics 1.2 Definition or Statistics 1.3 Importance and Scope of Statistics 1.4 Limitations or Statistics 2. Frequency Distributions and Mesures of Central Tendency 2.1 Frequency Distributions 2.2 Graphic Representation or Frequency Distribution 2.3 Averages or Measures of Central Tendency or Measures of Location 2.4 Requisites for an Ideal Measure of Central Tendency 2.5 Arithmetic Mean 2.6 Median 2.7 Mode 2.8 Geometric Mean 2.9 Harmonic Mean 2.10 Selection of an Average 2.11 Partition Values 3. Measures of Dispersion, Skewness and Kurtosis 3.1 Dispersion 3.2 Characteristics of an Ideal Measure of Dispersion 3.3 Measures of Dispersion 3.4 Range 3.5 Quartitle Deviation 3.6 Mean Deviation 3.7. Standard Deviation and Root Mean Square Deviation 3.8. Coefficient of Dispersion 3.9 Moments 3.10. Pearson's b and g Coefficients 3.11 Factorial Moments 3.12 Absolute Moments 3.13 Skewness 3.14 Kurtosis 4. Theory of Probability 4.1 Introduction 4.2 Short History 4.3 Definitions of Various Terms 4.4 Mathematical Tools: Preliminary Notions of Sets 4.5 Axiomatic Approach to Probability 4.6 Probability - Mathematical Notion 4.7 Multiplication Law of Probability and Conditional Probability 4.8 Bayes Theorem 4.9 Geometric probability 5. Random Variables-Distribution Functions 5.1 Random Variable 5.2 Distribution Function 5.3 Discrete Random Variable 5.4 Continuous Random Variable 5.5 Joint Probability Law 5.6 Transformation of One-dimensional Random Variable 5.7 Transformation of Two-dimensional Random Variable 6. Mathematical Expectation, Generating Functions and Law of Large Numbers 6.1 Mathematical Expectation 6.2 Expectation of a Function of a Random Variable 6.3 Addition Theorem of Expectation 6.4 Multiplication Theorem of Expectation 6.5 Expectation of a Linear Combiriation of Random Variables 6.6 Covariance 6.7 Variance of a Linear Combination of Random Variables 6.8 Moments of Bivariate Probability Distributions 6.9 Conditional Expectation and Conditional Variance 6.10 Moment Generating Function 6.11 Cumulants 6.12 Characteristic Function 6.13 Chebychev's Inequality 6.14 Convergence in probability 6.15 Weak Law of Large Numbers 6.16 Borel-Cantelli Lemma 6.17 Probability Generating Function 7. Theoretical Discrete Probability Distributions 7.0 Introduction 7.1 Bernoulli Distribution 7.2 Binomial Distribution 7.3 Poisson Distribution 7.4 Negative Binomial Distribution 7.5 Geometric: Distribution 7.6 Hypeometric Distribution 7.7 Multinomial Distribution 7.8 Discrete Uniform Distribution 7.9 Power Series Distribution 8. Theoretical Continuous Distributions 8.1 Rectangular (or Uniform Distribution) 8.2 Normal Distribution 8.3 Gamma Distribution 8.4 Beta Distribution of First Kind 8.5 Bela Distribution of Second Kind 8.6 The Exponential Distribution 8.7 Laplace (Double Exponential) Distribution 8.8. Weibul Distribution 8.9 Cauchy's Distribution 8.10 Central Limit Theorem 8.11 Compound distributions 8.12 Pearson's Distributions 8.13 Variate Tranformations 8.14 Order Statistics 8.15 Truncated Distributions 9. Curve Fitting and Principle of Least Squares 9.1 Curve Fitting 9.2 Most Plausible Solution of a System of Linear Equations 9.3 Conversion of Data to Linear Form 9.4 Selection of Type of Curve be Fitted 9.5 Curve Fitting by Orthogonal Polynomials 10. Correlation and Regression 10.1 Bivariate Distribution, Correlation 10.2 Scatter Diagram 10.3 Karl Pearson Coefficient or Correlation 10.4 Calculation of tbe Correlation Coefficient (or a Bivariate Frequency Distribution) 10.5 Probable Error of Correlation Coefficient 10.6 Rank Correlation 10.7 Regression 10.8 Correlation Ratio 10.9 Intra-class Correlation 10.10 Bivariate Normal Distribution 10.11 Multiple and Partial Correlation 10.12 Plane of Regression 10.13 Properties or Residuals 10.14 Coefficient of Multiple Correlation 10.15 Coefficient of Partial Correlation 10.16 Multiple Correlation in Terms or Total and Partial Correlations 10.17 Expression for Regression Coefficients in Terms of Regression Coefficients of Lower Order 10.18 Expression for Partial Correlation Coefficient in Terms of Correlation Coefficients of Lower Order 11. Theory of Attributes 11.1 Introduction 11.2 Notations 11.3 Dichotomy 11.4 Classes and Class Frequencies 11.5 Class Symbols as Operators 11.6 Consistenc of Data 11.7 Independence of Attributes 11.8 Associatio of Attributes 12. Sampling and Large Sample Tests 12.1 Sampling-Introduction 12.2 Types or Sampling 12.3 Parameter and Statistic 12.4 Tests of Significance 12.5 Null Hypothesis 12.6 Errors in Sampling 12.7 Critical Region and Level or Significance 12.8 Test of Significance for Large Samples 12.9 Sampling for Attributes 12.10 Sampling of Variables 12.11 Unbiased Estimate for population Mean and Variance 12.12 Standard Error of Sample Mean 12.13 Test of Significance for Single Mean 12.14 Test of Significance for Difference of Means 12.15 Test of Significance for the Difference of Standard Deviations 13. Exact Sampling Distributions (Chi-square Distribution) 13.1 Chi-Square Variate 13.2 Derivation or the Chi-square Distribution.First Method-Method of Moment Generating Function 13.3 M.G.F. of X2-distribution 13.4 Chi-square Probability Curve 13.5 Conditions for tbe Validity of X^2 test 13.6 Linear Transformatlon 13.7 Applications or Chi-square Distribution 13.8 Yates' Correction 13.9 Brandt and Snedecor Formula for 2 x k Contingency Table 13.10 Bartlett's Test for Homogeneity of Several Independent Estimates of the Same Population Variance 13.11 X2-Test for Pooling the Probabilities from Independent Tests to give a Single Test of Significance 13.12 Non-central X2-distribution 14. Exact Sampling Distributions (t, F AND Z DISTRIBUTIONS) 14.1 Introduction 14.2 Student's 't' 14.3 Distribution of Sample Correlation Coefficient when Population Correlation Coefficient rho = 0 14.4 Non-central t-distribution 14.5 F-statistic. Definition 14.6 Non-Central F-dlstribution 14.7 Fisher's z-distribution 14.8 Fisher's z-transformation 15. Statistical Inference I (Theory of Estimation) 15.1 Introduction 15.2 Characteristics of Estimators 15.3 Consistency 15.4 Unbiasedness 15.5 Efficient Estimators 15.6 Sufficiency 15.7 Cramer-Rao Inequality 15.8 Complete Family or Distributions 15.9 MVU and Blackwellisation 15.10 Methods of Estimation 15.11 Method of Maximum Likelihood Estimation 15.12 Method of Minimum Variance 15.13 Method ot Moments 15.14 Method of Least Squares 15.15 Confidence Interval and Confidence Limits 16. Statistical Infernce II (Testing of Hypothesis, Non-parametric Methods and Sequential Analysis J 16.1 Introduction 16.2 Statistical hypothesis-Simple and Composite 16.3 Steps in Solvlog Testiog of Hypothesis Problem 16.4 Optimum Test Under Different Situations 16.5 Neyman J. and Pearson, E.S. Lemma 16.6 Likelihood Ratio Test 16.7 How the Likelihood Ratio Criterion can be used to Obtain Various Standard tests of Significance 16.8 Non-parametric Methods 16.9 Sequential Analysis App.: Numerical Tables INDEX