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| 材料类型： | 互联网资源 |
|---|---|
| 文件类型： | 书, 互联网资源 |
| 所有的著者/提供者： |
Robert V Edwards |
| ISBN: | 9812568344 9789812568342 |
| OCLC号码： | 74815179 |
| 描述： | xi, 140 p. : ill. ; 24 cm. |
| 内容： | 1 Random Variables 1 -- 1.2 Expected Values 4 -- 1.3 Probability Distribution Functions 4 -- 1.3.1 Properties of probability density functions 10 -- 1.4 The Expected Value Process 11 -- 1.5 Variance and Standard Deviation 12 -- 1.6 Moments and Moment Generating Functions 14 -- 1.7 Common Types of Distributions 15 -- 1.7.1 Uniform distribution 15 -- 1.7.2 Binomial distribution 16 -- 1.7.2.1 Using the binomial distribution 19 -- 1.7.3 Poisson distribution 20 -- 1.7.4 Gaussian (or normal) distribution 23 -- 1.7.5 Student-t distribution 24 -- 1.7.6 Sum of two Gaussian variables 26 -- 1.7.7 The Chi-squared distribution 26 -- 1.7.8 The error function 27 -- 1.8 Functions of More Than One Random Variable 28 -- 1.8.1 (Bayes theorem) 28 -- 1.8.2 Joint Gaussian distributions 31 -- 1.9 Change of Variable 32 -- 2 Measurement of Samples of Random Numbers 37 -- 2.1 Variance of the Measured Mean 37 -- 2.2 Estimate of the Variance 39 -- 2.3 Variance of the Measured Variance 41 -- 2.4 Non-Independent Random Variables 45 -- 2.5 Histograms 47 -- 2.5.1 Statistical experiments involving the uniform and binomial distributions 48 -- 2.6 Confidence Limits 51 -- 2.6.1 Tests of hypotheses 53 -- 3 Time Series-Random Variables that are Functions of Time 61 -- 3.1 Averages 61 -- 3.2 The Autocovariance and Autocorrelation Function 62 -- 3.2.1 Variance of the average of a signal with correlation 63 -- 3.3 The Power Spectrum of a Random Signal 66 -- 3.3.1 Short review of Fourier transforms 67 -- 3.4 Processing Time Series by Computer 69 -- 3.5 Estimation of the Autocorrelation 70 -- 3.5.1 Error covariance for autocorrelation estimates 70 -- 3.5.2 Random, correlated signal generator 75 -- 3.6 Estimation of the Power Spectrum of Time Series Data 76 -- 3.6.1 Generic properties of the digital Fourier transform 77 -- 3.6.2 The variance of spectrum estimates 79 -- 3.7 Batch Mode Autocorrelation 82 -- 4 Parameter Estimation 87 -- 4.1 Motivation 87 -- 4.2 Maximum Likelihood Estimation 91 -- 4.2.1 Gaussian processes 92 -- 4.2.2 Poisson processes 94 -- 4.2.3 Non-independent Gaussian statistics 95 -- 4.2.4 Chi-squared distributions 97 -- 4.3 Residuals 98 -- 4.4 Parameter Error Estimates 100 -- 4.4.1 Expected errors for Gaussian statistics 103 -- 4.4.2 Error estimates for joint Gaussian statistics 105 -- 4.4.3 Error estimates for Poisson processes 106 -- 4.4.4 Error estimates for Chi-square distributions 106 -- 4.5 A Priori Error Estimation 106 -- 4.6 Maximum A Posteriori Estimation 108 -- 5 Random Sampling 115 -- 5.1 Basic Concepts of Random Sampling 115 -- 5.2 Independent Sampling 116 -- 5.2.1 Mean and variance of the mean with random sampling 117 -- 5.2.2 Spectrum and autocorrelation estimate using randomly sampled data 119 -- 5.2.3 Effect of finite sample intervals [Delta]t 124 -- 5.3 Sample and Hold Autocorrelation and Spectrum Estimation 124 -- 5.4 Non-Independent Sampling 127 -- 5.4.1 Sample and hold (rate depends on f) 129 -- 5.4.2 Controlled sampling 132 -- 5.4.3 Autocorrelation estimation 133 -- 5.5 Photon Detection 134 -- 5.5.1 Moments 134 -- 5.5.2 Autocorrelation estimation 135. |
| 责任： | Robert V. Edwards. |
| 更多信息： |
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