Preface |
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v | |
About the Authors |
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vii | |
Dedication |
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xi | |
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The Generalized Lambda Family of Distributions |
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1 | (40) |
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3 | (6) |
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Definition of the Generalized Lambda Distributions |
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9 | (2) |
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The Parameter Space of the GLD |
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11 | (10) |
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Shapes of the GLD Density Functions |
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21 | (16) |
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GLD Random Variate Generation |
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37 | (4) |
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38 | (3) |
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Fitting Distributions and Data with the GLD via the Method of Moments |
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41 | (72) |
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The Moments of the GLD Distribution |
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43 | (4) |
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The (α2 3, α4)-Space Covered by the GLD Family |
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47 | (6) |
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Fitting the GLD Through the Method of Moments |
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53 | (13) |
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Fitting through Direct Computation |
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54 | (9) |
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Fitting by the Use of Tables |
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63 | (1) |
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Limitations of the Method of Moments |
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64 | (2) |
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GLD Approximations of Some Well-Known Distributions |
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66 | (26) |
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67 | (1) |
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68 | (2) |
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The Student's t Distribution |
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70 | (1) |
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The Exponential Distribution |
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71 | (2) |
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The Chi-Square Distribution |
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73 | (2) |
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75 | (1) |
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76 | (2) |
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The Lognormal Distribution |
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78 | (1) |
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79 | (2) |
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The Inverse Gaussian Distribution |
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81 | (1) |
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The Logistic Distribution |
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82 | (2) |
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The Largest Extreme Value Distribution |
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84 | (1) |
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The Extreme Value Distribution |
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84 | (2) |
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The Double Exponential Distribution |
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86 | (1) |
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87 | (2) |
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89 | (1) |
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Summary of Distributions and their GLD fits |
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90 | (2) |
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Examples: GLD Fits of Data, Method of Moments |
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92 | (12) |
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Assessment of Goodness-of-Fit |
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93 | (3) |
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Example: Cadmium in Horse Kidneys |
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96 | (2) |
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Example: Brain (Left Thalamus) MRI Scan Data |
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98 | (1) |
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Example: Human Twin Data for Quantifying Genetic (vs. Environmental) Variance |
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99 | (3) |
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Example: Rainfall Distributions |
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102 | (2) |
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Moment-Based GLD Fit to Data from a Histogram |
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104 | (3) |
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The GLD and Design of Experiments |
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107 | (6) |
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111 | (2) |
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The Extended GLD System, the EGLD: Fitting by the Method of Moments |
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113 | (40) |
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The Beta Distribution and its Moments |
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113 | (6) |
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The Generalized Beta Distribution and its Moments |
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119 | (4) |
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Estimation of GBD (β1, β2, β3, β4) Parameters |
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123 | (6) |
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GBD Approximations of Some Well-Known Distributions |
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129 | (10) |
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130 | (1) |
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131 | (1) |
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The Student's t Distribution |
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131 | (1) |
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The Exponential Distribution |
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132 | (1) |
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The Chi-Square Distribution |
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133 | (1) |
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134 | (1) |
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134 | (2) |
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The Lognormal Distribution |
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136 | (1) |
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137 | (1) |
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The Inverse Gaussian Distribution |
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138 | (1) |
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The Logistic Distribution |
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138 | (1) |
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The Largest Extreme Value Distribution |
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138 | (1) |
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The Extreme Value Distribution |
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138 | (1) |
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The Double Exponential Distribution |
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139 | (1) |
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139 | (1) |
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139 | (1) |
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Examples: GBD Fits of Data, Method of Moments |
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139 | (11) |
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Example: Fitting a GBD to Simulated Data from GBD (3, 5, 0, -0.5) |
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140 | (1) |
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Example: Fitting a GBD to Data Simulated from GBD (2, 7, 1, 4) |
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141 | (2) |
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Example: Cadmium in Horse Kidneys |
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143 | (1) |
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Example: Rainfall Data of Section 2.5.5 |
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144 | (2) |
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Example: Tree Stand Heights and Diameters in Forestry |
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146 | (4) |
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EGLD Random Variate Generation |
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150 | (3) |
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151 | (2) |
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A Percentile-Based Approach to Fitting Distributions and Data with the GLD |
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153 | (64) |
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154 | (3) |
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The (ρ3, ρ4)-space of GLD (λ1, λ2, λ3, λ4) |
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157 | (6) |
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Estimation of GLD Parameters Through a Method of Percentiles |
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163 | (6) |
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GLD Approximations of Some Well-Known Distributions |
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169 | (27) |
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169 | (2) |
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171 | (1) |
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The Student's t Distribution |
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171 | (3) |
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The Exponential Distribution |
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174 | (2) |
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The Chi-Square Distribution |
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176 | (1) |
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177 | (2) |
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179 | (1) |
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The Lognormal Distribution |
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180 | (3) |
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183 | (1) |
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The Inverse Gaussian Distribution |
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184 | (2) |
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The Logistic Distribution |
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186 | (1) |
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The Largest Extreme Value Distribution |
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187 | (2) |
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The Extreme Value Distribution |
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189 | (1) |
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The Double Exponential Distribution |
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189 | (2) |
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191 | (1) |
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192 | (2) |
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Summary of Distribution Approximations |
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194 | (2) |
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Comparison of the Moment and Percentile Methods |
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196 | (7) |
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Examples: GLD Fits of Data via the Method of Percentiles |
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203 | (9) |
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Example: Data from the Cauchy Distribution |
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204 | (2) |
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Data on Radiation in Soil Samples |
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206 | (2) |
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Data on Velocities within Galaxies |
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208 | (1) |
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Rainfall Data of Sections 2.5.5 and 3.5.4 |
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208 | (4) |
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Percentile-Based GLD Fit of Data from a Histogram |
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212 | (5) |
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214 | (3) |
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GLD--2: The Bivariate GLD Distribution |
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217 | (56) |
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218 | (3) |
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Plackett's Method of Bivariate d.f. Construction: The GLD-2 |
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221 | (10) |
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Fitting the GLD-2 to Well-Known Bivariate Distributions |
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231 | (16) |
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The Bivariate Normal (BVN) Distribution |
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232 | (6) |
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Gumbel's Bivariate Exponential Type I (BVE) |
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238 | (1) |
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238 | (6) |
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Kibble's Bivariate Gamma (BVG) |
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244 | (3) |
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GLD-2 Fits: Distributions with Non-Identical Marginals |
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247 | (5) |
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Bivariate Gamma BVG with Non-Identical Marginals |
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247 | (1) |
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Bivariate with Normal and Cauchy Marginals |
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247 | (2) |
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Bivariate with Gamma and ``Backwards Gamma'' Marginals |
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249 | (3) |
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Fitting GLD-2 to Datasets |
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252 | (13) |
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Algorithm for Fitting the GLD-2 to Data |
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252 | (8) |
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Example: Human Twin Data of Section 2.5.4 |
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260 | (2) |
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Example: The Rainfall Distributions of Section 2.5.5 |
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262 | (2) |
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Example: The Tree Stand Data of Section 3.5.5 |
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264 | (1) |
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GLD-2 Random Variate generation |
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265 | (4) |
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Conclusions and Research Problems Regarding GLD-2 |
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269 | (4) |
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271 | (2) |
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The Generalized Bootstrap (GB) and Monte Carlo (MC) Methods |
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273 | (12) |
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The Generalized Bootstrap (GB) Method |
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274 | (8) |
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Comparisons of the GB and BM Methods |
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282 | (3) |
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282 | (3) |
Appendices |
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285 | (132) |
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A Programs for Fitting the GLD, GBD, and GLD-2 |
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285 | (24) |
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A.1 General Utility Programs |
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287 | (4) |
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A.2 GLD Parameter Estimation: Method of Moments |
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291 | (3) |
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A.3 GBD Parameter Estimation: Method of Moments |
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294 | (2) |
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A.4 GLD Parameter Estimation: Method of Percentiles |
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296 | (2) |
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A.5 Programs for GLD-2 Fitting |
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298 | (11) |
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B Table B-1 for GLD Fits: Method of Moments |
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309 | (22) |
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C Table C-1 for GBD Fits: Method of Moments |
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331 | (26) |
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D Tables for GLD Fits: Method of Percentiles |
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357 | (56) |
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E The Normal Distribution |
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413 | (4) |
References and Author Index |
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417 | (12) |
Subject Index |
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429 | |