Preface |
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xiii | |
About the Author |
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xix | |
Supplementary Material |
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xxi | |
Part 1: The Basics |
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1 | (314) |
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3 | (2) |
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2 Application to Process Control |
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5 | (6) |
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5 | (2) |
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2.2 Inferential Properties |
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7 | (1) |
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2.3 Controller Performance Monitoring |
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7 | (1) |
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8 | (1) |
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9 | (2) |
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11 | (12) |
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11 | (1) |
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11 | (1) |
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12 | (5) |
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17 | (1) |
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17 | (1) |
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3.6 Fuel Gas Heating Value |
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18 | (1) |
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19 | (3) |
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22 | (1) |
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4 Characteristics of Data |
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23 | (28) |
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23 | (1) |
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24 | (1) |
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4.3 Use of Historical Data |
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24 | (1) |
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25 | (7) |
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32 | (1) |
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33 | (2) |
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35 | (2) |
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4.8 Skewness and Kurtosis |
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37 | (9) |
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46 | (1) |
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47 | (4) |
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5 Probability Density Function |
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51 | (32) |
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55 | (2) |
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5.2 Triangular Distribution |
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57 | (2) |
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59 | (3) |
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5.4 Bivariate Normal Distribution |
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62 | (3) |
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5.5 Central Limit Theorem |
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65 | (4) |
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5.6 Generating a Normal Distribution |
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69 | (1) |
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70 | (1) |
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71 | (2) |
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73 | (1) |
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5.10 Combined Distribution |
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73 | (2) |
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5.11 Compound Distribution |
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75 | (1) |
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5.12 Generalised Distribution |
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75 | (1) |
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5.13 Inverse Distribution |
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76 | (1) |
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5.14 Transformed Distribution |
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76 | (1) |
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5.15 Truncated Distribution |
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77 | (1) |
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5.16 Rectified Distribution |
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78 | (1) |
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5.17 Noncentral Distribution |
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78 | (1) |
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79 | (1) |
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80 | (3) |
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83 | (22) |
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6.1 Box and Whisker Diagram |
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83 | (1) |
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84 | (6) |
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6.3 Kernel Density Estimation |
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90 | (5) |
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95 | (2) |
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97 | (1) |
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98 | (1) |
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98 | (7) |
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105 | (8) |
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105 | (1) |
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106 | (1) |
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7.3 Skewness and Kurtosis |
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107 | (1) |
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108 | (2) |
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110 | (3) |
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113 | (14) |
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113 | (3) |
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116 | (2) |
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118 | (1) |
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119 | (1) |
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120 | (1) |
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121 | (1) |
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122 | (1) |
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8.8 Instrumentation Error |
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123 | (4) |
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127 | (20) |
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9.1 Accuracy of Mean and Standard Deviation |
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130 | (1) |
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131 | (3) |
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134 | (1) |
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135 | (3) |
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9.5 Fitting to a Histogram |
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138 | (3) |
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9.6 Choice of Penalty Function |
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141 | (6) |
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10 Distribution of Dependent Variables |
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147 | (18) |
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10.1 Addition and Subtraction |
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147 | (1) |
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10.2 Division and Multiplication |
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148 | (5) |
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153 | (1) |
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10.4 Logarithmic and Exponential Functions |
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153 | (9) |
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162 | (2) |
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10.6 Trigonometric Functions |
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164 | (1) |
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11 Commonly Used Functions |
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165 | (20) |
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165 | (1) |
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11.2 Euler-Mascheroni Constant |
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166 | (1) |
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166 | (1) |
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167 | (1) |
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168 | (6) |
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174 | (1) |
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174 | (2) |
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176 | (2) |
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178 | (2) |
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11.10 Riemann Zeta Function |
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180 | (1) |
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180 | (2) |
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11.12 Stirling Approximation |
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182 | (1) |
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183 | (2) |
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12 Selected Distributions |
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185 | (50) |
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186 | (3) |
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189 | (2) |
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191 | (4) |
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195 | (9) |
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204 | (4) |
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208 | (2) |
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210 | (3) |
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213 | (3) |
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216 | (5) |
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221 | (4) |
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225 | (6) |
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231 | (4) |
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13 Extreme Value Analysis |
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235 | (10) |
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245 | (8) |
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253 | (6) |
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259 | (32) |
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275 | (3) |
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278 | (1) |
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16.3 Akaike Information Criterion |
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279 | (2) |
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16.4 Artificial Neural Networks |
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281 | (5) |
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286 | (5) |
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291 | (8) |
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299 | (6) |
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305 | (10) |
Part 2: Catalogue of Distributions |
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315 | (254) |
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317 | (32) |
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317 | (3) |
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320 | (1) |
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320 | (1) |
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321 | (1) |
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321 | (2) |
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323 | (2) |
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325 | (4) |
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20.8 Generalised Inverse Gaussian |
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329 | (1) |
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20.9 Normal Inverse Gaussian |
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330 | (2) |
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20.10 Reciprocal Inverse Gaussian |
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332 | (2) |
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334 | (4) |
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338 | (7) |
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20.13 Exponentially Modified Gaussian |
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345 | (2) |
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347 | (2) |
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349 | (12) |
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349 | (1) |
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349 | (1) |
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349 | (1) |
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350 | (1) |
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351 | (1) |
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351 | (2) |
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353 | (1) |
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354 | (1) |
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354 | (1) |
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355 | (1) |
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356 | (1) |
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356 | (1) |
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357 | (4) |
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361 | (16) |
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361 | (3) |
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364 | (1) |
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365 | (2) |
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367 | (2) |
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369 | (1) |
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22.6 Inverse Paralogistic |
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370 | (1) |
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22.7 Generalised Logistic |
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371 | (4) |
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22.8 Generalised Log-Logistic |
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375 | (1) |
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22.9 Exponentiated Kumaraswamy-Dagum |
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376 | (1) |
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377 | (12) |
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377 | (1) |
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23.2 Bounded Pareto Type I |
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378 | (1) |
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379 | (2) |
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381 | (1) |
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381 | (1) |
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382 | (1) |
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383 | (1) |
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383 | (2) |
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385 | (4) |
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389 | (4) |
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389 | (1) |
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389 | (2) |
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391 | (1) |
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391 | (1) |
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392 | (1) |
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393 | (16) |
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393 | (1) |
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394 | (1) |
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395 | (1) |
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396 | (1) |
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396 | (3) |
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25.6 Generalised Beta Prime |
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399 | (1) |
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400 | (1) |
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401 | (2) |
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403 | (1) |
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404 | (3) |
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407 | (2) |
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409 | (6) |
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409 | (1) |
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410 | (2) |
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412 | (1) |
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412 | (1) |
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413 | (2) |
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415 | (20) |
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416 | (1) |
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416 | (1) |
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417 | (1) |
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418 | (6) |
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424 | (1) |
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425 | (4) |
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429 | (4) |
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433 | (1) |
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433 | (1) |
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433 | (1) |
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434 | (1) |
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434 | (1) |
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28 Exponential Distribution |
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435 | (12) |
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28.1 Generalised Exponential |
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435 | (1) |
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435 | (1) |
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436 | (1) |
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437 | (1) |
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438 | (1) |
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439 | (1) |
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439 | (1) |
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28.8 Stretched Exponential |
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440 | (1) |
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28.9 Exponential Logarithmic |
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441 | (1) |
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28.10 Logistic Exponential |
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442 | (1) |
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442 | (3) |
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445 | (2) |
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447 | (4) |
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447 | (1) |
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447 | (4) |
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451 | (12) |
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451 | (1) |
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452 | (2) |
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454 | (1) |
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454 | (4) |
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458 | (1) |
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459 | (1) |
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30.7 Noncentral Chi-Squared |
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460 | (3) |
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463 | (8) |
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463 | (1) |
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463 | (4) |
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467 | (1) |
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468 | (3) |
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32 Symmetrical Distributions |
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471 | (16) |
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471 | (1) |
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472 | (1) |
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473 | (2) |
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475 | (1) |
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476 | (1) |
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477 | (1) |
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478 | (1) |
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479 | (2) |
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481 | (1) |
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481 | (2) |
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483 | (3) |
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486 | (1) |
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33 Asymmetrical Distributions |
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487 | (38) |
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487 | (1) |
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488 | (2) |
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490 | (1) |
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491 | (1) |
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492 | (2) |
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494 | (2) |
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496 | (1) |
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497 | (1) |
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498 | (1) |
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499 | (1) |
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499 | (3) |
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502 | (2) |
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504 | (2) |
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506 | (1) |
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507 | (2) |
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33.16 Generalised Lindley |
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509 | (1) |
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509 | (1) |
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510 | (2) |
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512 | (1) |
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513 | (1) |
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514 | (2) |
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516 | (1) |
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517 | (1) |
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517 | (2) |
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33.25 Generalised Tukey Lambda |
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519 | (2) |
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521 | (4) |
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525 | (4) |
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529 | (20) |
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529 | (2) |
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531 | (1) |
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531 | (4) |
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535 | (1) |
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536 | (2) |
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538 | (2) |
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35.7 Beta-Negative Binomial |
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540 | (1) |
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541 | (1) |
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542 | (1) |
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35.10 Conway-Maxwell-Poisson |
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543 | (3) |
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546 | (3) |
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36 Other Discrete Distributions |
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549 | (20) |
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549 | (3) |
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552 | (3) |
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555 | (1) |
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556 | (2) |
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558 | (1) |
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559 | (2) |
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36.7 Negative Hypergeometric |
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561 | (1) |
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561 | (2) |
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563 | (1) |
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564 | (1) |
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565 | (2) |
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567 | (2) |
Appendix 1 Data Used in Examples |
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569 | (8) |
Appendix 2 Summary of Distributions |
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577 | (14) |
References |
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591 | (2) |
Index |
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593 | |