Handbook of statistical distributions with applications

Handbook of Statistical Distributions with Applications......Page 1
STATISTICS: Textbooks and Monographs......Page 4
Preface......Page 6
Contents......Page 8
0.1 Introduction......Page 21
0.2 Contents of StatCalc......Page 24
1.1 Random Variables and Expectations......Page 28
1.2.2 Moments......Page 31
1.2.3 Measures of Variability......Page 32
1.2.5 Other Measures......Page 33
1.3 Some Functions Relevant to Reliability......Page 34
1.4 Model Fitting......Page 35
1.4.2 The Chi-Square Goodness-of-Fit Test......Page 36
1.5.1 Moment Estimation......Page 37
Some Terminologies......Page 38
Errors and Powers......Page 39
Tolerance Intervals......Page 42
The Accept/Reject Method......Page 43
1.8 Some Special Functions......Page 44
2.1 Description......Page 47
2.2 Moments......Page 48
3.1 Description......Page 49
3.2 Moments......Page 50
3.3 Computing Table Values......Page 52
Illustrative Examples......Page 53
3.4.2 Power of the Exact Test......Page 54
3.5.1 An Exact Confidence Interval......Page 56
3.5.2 Computing Exact Limits and Sample Size Calculation......Page 57
3.6.1 An Unconditional Test......Page 58
3.6.2 Power of the Unconditional Test......Page 59
3.7 Fisher's Exact Test......Page 60
3.7.1 Calculation of p-Values......Page 61
3.7.2 Exact Powers......Page 62
3.8.2 Relation to Other Distributions......Page 63
3.9 Random Number Generation......Page 64
3.10 Computation of Probabilities......Page 66
4.1 Description......Page 69
4.2 Moments......Page 70
4.3 Computing Table Values......Page 72
Illustrative Examples......Page 73
4.4 Point Estimation......Page 74
4.5.1 An Exact Test......Page 75
4.5.2 Power of the Exact Test......Page 76
4.6.1 Confidence Intervals......Page 77
Expected Length......Page 78
4.7.1 The Test......Page 80
4.7.2 Power Calculation......Page 81
4.8.3 Approximations......Page 82
4.9 Random Number Generation......Page 83
4.10 Computation of Probabilities......Page 84
5.1 Description......Page 88
5.2 Moments......Page 89
5.3 Computing Table Values......Page 91
5.5.1 An Exact Test......Page 92
5.5.2 Powers of the Exact Test......Page 93
5.6.1 An Exact Confidence Interval......Page 94
5.7.1 A Conditional Test......Page 95
5.7.2 Powers of the Conditional Test......Page 97
5.9 A Test for the Difference between Two Means......Page 98
5.9.1 An Unconditional Test......Page 99
5.9.2 Powers of the Unconditional Test......Page 100
5.10 Model Fitting with Examples......Page 101
5.11.2 Relation to Other Distributions......Page 103
5.12 Random Number Generation......Page 104
5.13 Computation of Probabilities......Page 105
6.1 Description......Page 109
6.3 Computing Table Values......Page 110
6.4 Properties and Results......Page 111
6.5 Random Number Generation......Page 112
7.1 Description......Page 113
7.2 Moments......Page 114
Illustrative Examples......Page 116
7.5 A Test for the Proportion......Page 117
7.7.1 Properties......Page 119
7.8 Random Number Generation......Page 120
7.9 A Computational Method for Probabilities......Page 122
8.1 Description......Page 123
8.3 Computing Table Values......Page 125
8.4.2 Interval Estimation......Page 128
8.6 Random Number Generation......Page 129
8.7 A Computational Algorithm for Probabilities......Page 130
9.1 Description......Page 131
9.3 Inferences......Page 132
9.5 Random Number Generation......Page 133
10.1 Description......Page 134
An Example for Model Checking......Page 135
10.3 Computing Table Values......Page 138
Some Illustrative Examples......Page 140
10.4.1 Point Estimation......Page 142
Power Computation......Page 143
10.4.3 Interval Estimation for the Mean......Page 145
Some Illustrative Examples......Page 146
Test about a Normal Variance......Page 147
Confidence Interval for a Normal Variance......Page 148
10.5 Two-Sample Inference......Page 149
Interval Estimation for the Ratio of Variances......Page 150
10.5.2 Inference for the Difference between Two Means when the Variances are Equal......Page 151
Power of the Two-Sample t-test......Page 152
Interval Estimation of u1 -- u2......Page 153
10.5.3 Inference for the Difference between Two Means......Page 155
10.6.1 Two-Sided Tolerance Intervals......Page 157
10.6.2 One-Sided Tolerance Limits......Page 158
Applications......Page 159
10.6.3 Equal-Tail Tolerance Intervals......Page 160
10.6.4 Simultaneous Hypothesis Testing for Quantiles......Page 161
10.6.5 Tolerance Limits for One-Way Random E®ects Model......Page 162
10.7 Properties and Results......Page 164
10.8 Relation to Other Distributions......Page 165
10.9 Random Number Generation......Page 166
10.10 Computing the Distribution Function......Page 168
11.1 Description......Page 170
11.2 Moments......Page 171
11.4 Applications......Page 172
11.5.1 Properties......Page 173
11.5.2 Relation to Other Distributions......Page 174
11.5.3 Approximations......Page 175
11.7 Computing the Distribution Function......Page 176
12.1 Description......Page 177
12.3 Computing Table Values......Page 179
12.4.2 Relation to Other Distributions......Page 180
12.4.3 Series Expansions......Page 181
12.5 Random Number Generation......Page 182
12.6 A Computational Method for Probabilities......Page 183
13.1 Description......Page 184
13.2 Moments......Page 185
13.4 Distribution of the Maximum of Several /t/ Variables......Page 186
Simultaneous Con¯dence Intervals for the Treatment Means......Page 187
13.4.3 An Example......Page 188
13.5.2 Relation to Other Distributions......Page 189
13.5.3 Series Expansions for Cumulative Probability......Page 190
13.7 A Computational Method for Probabilities......Page 191
14.1 Description......Page 192
14.3 Computing Table Values......Page 193
Con¯dence Intervals......Page 194
14.5.2 Relation to Other Distributions......Page 195
14.6 Random Number Generation......Page 196
15.1 Description......Page 197
15.2 Moments......Page 198
15.3 Computing Table Values......Page 199
15.4 Applications with Some Examples......Page 200
15.5.1 Maximum Likelihood Estimators......Page 201
15.5.3 Interval Estimation......Page 202
15.6 Properties and Results......Page 203
15.7 Random Number Generation......Page 204
15.8 A Computational Method for Probabilities......Page 205
16.1 Description......Page 207
16.2 Moments......Page 208
16.3 Computing Table Values......Page 209
16.5 Applications with an Example......Page 210
16.6.1 An Identity and Recurrence Relations......Page 213
16.6.2 Relation to Other Distributions......Page 214
16.7 Random Number Generation......Page 215
16.8 Evaluating the Distribution Function......Page 217
17.1 Description......Page 219
17.3 Computing Table Values......Page 221
17.4 Applications......Page 222
17.5.3 Approximations to Percentiles......Page 223
17.7 Evaluating the Distribution Function......Page 224
18.1 Description......Page 228
18.4 Applications......Page 230
18.5.1 Properties......Page 231
18.6 Random Number Generation......Page 232
18.7 Evaluating the Distribution Function......Page 233
19.1 Description......Page 236
19.2 Moments......Page 237
19.4 Applications......Page 238
19.5.1 Properties......Page 239
19.7 Evaluating the Distribution Function......Page 240
20.1 Description......Page 244
20.2 Moments......Page 245
20.4.1 Maximum Likelihood Estimators......Page 246
20.5 Applications......Page 247
20.6 Relation to Other Distributions......Page 249
20.7 Random Number Generation......Page 250
21.1 Description......Page 251
21.2 Moments......Page 252
21.3 Computing Table Values......Page 253
21.5 Applications......Page 254
21.7 Random Number Generation......Page 255
22.1 Description......Page 256
22.2 Moments......Page 257
22.3 Computing Table Values......Page 258
22.5 Confidence Interval and Test for the Mean......Page 259
22.6 Inferences for the Difference between Two Means......Page 260
Illustrative Examples......Page 261
22.7 Inferences for the Ratio of Two Means......Page 262
22.9 Properties and Results......Page 263
22.11 Computation of Probabilities and Percentiles......Page 264
23.1 Description......Page 266
23.2 Moments......Page 267
23.4 Inferences......Page 268
23.5 Applications......Page 269
23.8 Computation of Probabilities and Percentiles......Page 270
24.1 Description......Page 271
24.2 Moments......Page 272
24.4 Applications......Page 273
24.5 Point Estimation......Page 274
24.8 Computation of Probabilities and Percentiles......Page 275
25.1 Description......Page 276
25.2 Moments......Page 277
25.4 Maximum Likelihood Estimators......Page 278
25.5 Applications......Page 279
25.8 Computation of Probabilities and Percentiles......Page 280
26.1 Description......Page 281
26.3 Computing Table Values......Page 282
26.4.1 Estimation Based on Sample Quantiles......Page 283
26.6 Properties and Results......Page 284
26.8 Computation of Probabilities and Percentiles......Page 285
27.1 Description......Page 286
27.2 Moments......Page 287
27.4 One-Sample Inference......Page 288
27.4.2 Confidence Interval for the Mean......Page 289
27.5.1 Inferences for the Di®erence between Two Mean......Page 290
27.6 Random Number Generation......Page 292
27.7 Computational Methods for Probabilities and Percentiles......Page 293
28.1 Description......Page 294
28.3 Computing Table Values......Page 295
28.5 Relation to Other Distributions......Page 296
28.6 Random Number Generation......Page 297
29.1 Description......Page 298
29.2 Computing Table Values......Page 299
29.3 An Example......Page 300
29.4 Inferences on Correlation Coe±cients......Page 301
An Exact Test......Page 302
A Generalized Variable Test......Page 303
An Exact Confidence Interval......Page 304
The Generalized Confidence Interval for p......Page 305
An Asymptotic Approach......Page 306
Generalized Test and Confidence Limits for p1 --p2......Page 307
29.6 Random Number Generation......Page 308
29.7 A Computational Algorithm for Probabilities......Page 310
30.1 Description......Page 311
Moments......Page 312
30.3 Examples......Page 313
31.1 Hypothesis Test for the Median......Page 315
31.3 Computing Table Values......Page 316
31.4 An Example......Page 317
32.1 Description......Page 318
32.2 Moments and an Approximation......Page 319
32.4 An Example......Page 320
33.1 Description......Page 322
33.3 Mann-Whitney U Statistic......Page 323
33.5 An Example......Page 324
34.1 Description......Page 326
34.3 An Example......Page 327
35.1 Description......Page 328
35.3 Examples......Page 329
36.1 Description......Page 331
36.3.1 Point Estimation......Page 332
36.3.3 Hypothesis Testing......Page 333
36.6 A Computational Method for Probabilities......Page 334
36.7 Computing Table Values......Page 336
References......Page 337