Handbook of statistical distributions with applications:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2006
|
| Series: | Statistics
188 |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | 346 S. Ill. 24 cm. + 1 CD-ROM, 12 cm |
| ISBN: | 1584886358 9781584886358 |
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| 245 | 1 | 0 | |a Handbook of statistical distributions with applications |c K. Krishnamoorthy |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2006 | |
| 300 | |a 346 S. |b Ill. |c 24 cm. + |e 1 CD-ROM, 12 cm | ||
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| 490 | 1 | |a Statistics |v 188 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Distribution (Théorie des probabilités) - Guides, manuels, etc | |
| 650 | 7 | |a Verdelingen (statistiek) |2 gtt | |
| 650 | 4 | |a Distribution (Probability theory) |v Handbooks, manuals, etc | |
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| adam_text | Contents
INTRODUCTION
TO STATCALC
0.1
Introduction
.........
0.2
Contents of StatCalc.
1
PRELIMINARIES
1.1
Random Variables and Expectations
...............................9
1.2
Moments and Other Functions
....................................12
1.2.1
Measures of Central Tendency
.............................12
1.2.2
Moments
..................................................12
1.2.3
Measures of Variability
....................................13
1.2.4
Measures of Relative Standing
.............................14
1.2.5
Other Measures
...........................................14
1.2.6
Some Other Functions
.....................................15
1.3
Some Functions Relevant to Reliability
...........................15
1.4
Model Fitting
....................................................16
1.4.1
Q-Q Plot
..................................................17
1.4.2
The Chi-Square Goodness-of-Fit Test
......................17
1.5
Methods of Estimation
...........................................18
1.5.1
Moment Estimation
.......................................18
1.5.2
Maximum Likelihood Estimation
..........................19
1.6
Inference
.........................................................19
1.6.1
Hypothesis Testing
........................................19
1.6.2
Interval Estimation
........................................23
1.7
Random Number Generation
.....................................24
1.8
Some Special Functions
...........................................25
2
DISCRETE UNIFORM
DISTRIBUTION
2.1
Description
.......................................................29
2.2
Moments
........................................................
ЗО
3
BINOMIAL
DISTRIBUTION
3.1
Description
.......................................................31
3.2
Moments
.........................................................32
3.3
Computing Table Values
..........................................34
3.4
Test for the
Proportion
...........................................36
3.4.1
An Exact Test
.............................................36
3.4.2
Power
of the
Exact Test
...................................36
3.5
Confidence
Intervals for the
Proportion
...........................38
3.5.1
An Exact Confidence
Interval
..............................38
3.5.2
Computing Exact
Limits and Sample Size Calculation
.....39
3.6
A
Test for the Difference between Two Proportions
...............40
3.6.1
An Unconditional Test
.....................................40
3.6.2
Power of the Unconditional Test
...........................41
3.7
Fisher s Exact Test
...............................................42
3.7.1
Calculation of p-Values
....................................43
3.7.2
Exact Powers
..............................................44
3.8
Properties and Results
............................................45
3.8.1
Properties
.................................................45
3.8.2
Relation to Other Distributions
............................45
3.8.3
Approximations
...........................................46
3.9
Random Number Generation
.....................................46
3.10
Computation of Probabilities
.....................................48
4
HYPERGEOMETRIC DISTRIBUTION
4.1
Description
.......................................................51
4.2
Moments
.........................................................52
4.3
Computing Table Values
..........................................54
4.4
Point Estimation
.................................................56
4.5
Test for the Proportion
...........................................57
4.5.1
An Exact Test
.............................................57
4.5.2
Power of the Exact Test
...................................58
4.6
Confidence Intervals and Sample Size Calculation
.................59
4.6.1
Confidence Intervais
.......................................59
4.6.2
Sample
Size for Precision
..................................60
4.7
A Test for the Difference between Two Proportions
...............62
4.7.1
The Test
..................................................62
4.7.2
Power Calculation
.........................................63
4.8
Properties and Results
............................................64
4.8.1
Recurrence Relations
......................................64
4.8.2
Relation to Other Distributions
............................64
4.8.3
Approximations
...........................................64
4.9
Random Number Generation
.....................................65
4.10
Computation of Probabilities
.....................................66
5
POISSON
DISTRIBUTION
5.1
Description
.......................................................71
5.2
Moments
.........................................................72
5.3
Computing Table Values
..........................................74
5.4
Point Estimation
.................................................75
5.5
Test for the Mean
................................................75
5.5.1
An Exact Test
.............................................75
5.5.2
Powers of the Exact Test
..................................76
5.6
Confidence Intervals for the Mean
................................77
5.6.1
An Exact Confidence Interval
..............................77
5.6.2
Sample Size Calculation for Precision
......................78
5.7
Test for the Ratio of Two Means
..................................78
5.7.1
A Conditional Test
........................................78
5.7.2
Powers of the Conditional Test
............................80
5.8
Confidence Intervals for the Ratio of Two Means
..................81
5.9
A Test for the Difference between Two Means
.....................81
5.9.1
An Unconditional Test
.....................................82
5.9.2
Powers of the Unconditional Test
..........................83
5.10
Model Fitting with Examples
.....................................84
5.11
Properties and Results
............................................86
5.11.1
Properties
................................................86
5.11.2
Relation to Other Distributions
...........................86
5.11.3
Approximations
..........................................87
5.12
Random Number Generation
.....................................87
5.13
Computation of Probabilities
.....................................88
6
GEOMETRIC
DISTRIBUTION
6.1
Description
.......................................................93
6.2
Moments
.........................................................94
6.3
Computing Table Values
..........................................94
6.4
Properties and Results
............................................95
6.5
Random Number Generation
......................................96
7
NEGATIVE BINOMIAL DISTRIBUTION
7.1
Description
.......................................................97
7.2
Moments
.........................................................98
7.3
Computing Table Values
.........................................100
7.4
Point Estimation
................................................101
7.5
A Test for the Proportion
.......................................101
7.6
Confidence Intervals for the Proportion
..........................103
7.7
Properties and Results
...........................................103
7.7.1
Properties
................................................103
7.7.2
Relation to Other Distributions
...........................104
7.8
Random Number Generation
....................................104
7.9
A Computational Method for Probabilities
.......................106
8
LOGARITHMIC SERIES DISTRIBUTION
8.1
Description
......................................................107
8.2
Moments
........................................................109
8.3
Computing Table Values
.........................................109
8.4
Inferences
.......................................................112
8.4.1
Point Estimation
.........................................112
8.4.2
Interval Estimation
.......................................112
8.5
Properties and Results
...........................................113
8.6
Random Number Generation
....................................113
8.7
A Computational Algorithm for Probabilities
....................114
9
UNIFORM DISTRIBUTION
9.1
Description
......................................................115
9.2
Moments
........................................................116
9.3
Inferences
.......................................................116
9.4
Properties and Results
...........................................117
9.5
Random Number Generation
....................................117
10
NORMAL DISTRIBUTION
10.1
Description
.....................................................119
10.2
Moments
.......................................................123
10.3
Computing Table Values
.......................................123
10.4
One-Sample Inference
..........................................127
10.4.1
Point Estimation
.......................................127
10.4.2
Test for the Mean and Power Computation
.............128
10.4.3
Interval Estimation for the Mean
.......................130
10.4.4
Test and Interval Estimation for the Variance
...........132
10.5
Two-Sample Inference
..........................................134
10.5.1
Inference for the Ratio of Variances
.....................135
10.5.2
Inference for the Difference between Two Means
when the Variances Are Equal
..........................136
10.5.3
Inference for the Difference between Two Means
.......140
10.6
Tolerance Intervals
.............................................142
10.6.1
Two-Sided Tolerance Intervals
..........................142
10.6.2
One-Sided Tolerance Limits
.............................143
10.6.3
Equal-Tail Tolerance Intervals
..........................145
10.6.4
Simultaneous Hypothesis Testing for Quantiles
..........146
10.6.5
Tolerance Limits for One-Way Random Effects Model.
.. 147
10.7
Properties and Results
.........................................149
10.8
Relation to Other Distributions
.................................150
10.9
Random Number Generation
...................................151
10.10
Computing the Distribution Function
...........................152
11
CHI-SQUARE DISTRIBUTION
11.1
Description
.....................................................155
11.2
Moments
.......................................................156
11.3
Computing Table Values
.......................................157
11.4
Applications
....................................................157
11.5
Properties and Results
.........................................158
11.5.1
Properties
..............................................158
11.5.2
Relation to Other Distributions
.........................159
11.5.3
Approximations
........................................160
11.6
Random Number Generation
...................................161
11.7
Computing the Distribution Function
...........................161
12
F DISTRIBUTION
12.1
Description
.....................................................163
12.2
Moments
.......................................................165
12.3
Computing Table Values
.......................................165
12.4
Properties and Results
.........................................166
12.4.1
Identities................................................
166
12.4.2
Relation
to Other
Distributions
.........................166
12.4.3
Series
Expansions
.......................................167
12.4.4
Approximations
........................................168
12.5
Random Number Generation
...................................168
12.6
A Computational Method for Probabilities
.....................169
13
STUDENT S
t
DISTRIBUTION
13.1
Description
.....................................................171
13.2
Moments
.......................................................172
13.3
Computing Table Values
.......................................173
13.4
Distribution of the Maximum of Several |t| Variables
...........173
13.4.1
An Application
.........................................174
13.4.2
Computing Table Values
................................175
13.4.3
An Example
............................................175
13.5
Properties and Results
.........................................176
13.5.1
Properties
..............................................176
13.5.2
Relation to Other Distributions
.........................176
13.5.3
Series Expansions for Cumulative Probability
...........177
13.5.4
An Approximation
.....................................178
13.6
Random Number Generation
...................................178
13.7
A Computational Method for Probabilities
.....................178
14
EXPONENTIAL DISTRIBUTION
14.1
Description
.....................................................179
14.2
Moments
.......................................................180
14.3
Computing Table Values
.......................................180
14.4
Inferences
......................................................181
14.5
Properties and Results
.........................................182
14.5.1
Properties
..............................................182
14.5.2
Relation to Other Distributions
.........................182
14.6
Random Number Generation
...................................183
15
GAMMA
DISTRIBUTION
15.1
Description
.....................................................185
15.2
Moments
....................................................... 186
15.3
Computing Table Values
.......................................187
15.4
Applications
with Some Examples
..............................188
15.5
Inferences
......................................................189
15.5.1
Maximum Likelihood Estimators
.......................189
15.5.2
Moment Estimators
....................................190
15.5.3
Interval Estimation
.....................................190
15.6
Properties and Results
.........................................191
15.7
Random Number Generation
...................................192
15.8
A Computational Method for Probabilities
.....................193
16
BETA DISTRIBUTION
16.1
Description
......................................................195
16.2
Moments
.......................................................196
16.3
Computing Table Values
.......................................197
16.4
Inferences
......................................................198
16.5
Applications with an Example
..................................198
16.6
Properties and Results
.........................................201
16.6.1
An Identity and Recurrence Relations
..................201
16.6.2
Relation to Other Distributions
.........................202
16.7
Random Number Generation
...................................203
16.8
Evaluating the Distribution Function
...........................205
17
NONCENTRAL
CHI-SQUARE DISTRIBUTION
17.1
Description
.....................................................207
17.2
Moments
.......................................................209
17.3
Computing Table Values
.......................................209
17.4
Applications
....................................................210
17.5
Properties and Results
.........................................211
17.5.1
Properties
..............................................211
17.5.2
Approximations to Probabilities
........................211
17.5.3
Approximations to Percentiles
..........................211
17.6
Random Number Generation
...................................212
17.7
Evaluating the Distribution Function
...........................212
18
NONCENTRAL F
DISTRIBUTION
18.1
Description
.....................................................217
18.2
Moments
.......................................................219
18.3
Computing Table Values
.......................................219
18.4
Applications
....................................................219
18.5
Properties and Results
.........................................220
18.5.1
Properties..............................................
220
18.5.2
Approximations
........................................221
18.6
Random Number Generation
...................................221
18.7
Evaluating the Distribution Function
...........................222
19
NONCENTRAL t
DISTRIBUTION
19.1
Description
.....................................................225
19.2
Moments
.......................................................226
19.3
Computing Table Values
.......................................227
19.4
Applications
....................................................227
19.5
Properties and Results
.........................................228
19.5.1
Properties
..............................................228
19.5.2
An Approximation
.....................................229
19.6
Random Number Generation
...................................229
19.7
Evaluating the Distribution Function
...........................229
20
LAPLACE DISTRIBUTION
20.1
Description
.....................................................233
20.2
Moments
.......................................................234
20.3
Computing Table Values
.......................................235
20.4
Inferences
......................................................235
20.4.1
Maximum Likelihood Estimators
.......................235
20.4.2
Interval Estimation
.....................................236
20.5
Applications
....................................................236
20.6
Relation to Other Distributions
.................................238
20.7
Random Number Generation
..................................239
21
LOGISTIC
DISTRIBUTION
21.1
Description
.....................................................241
21.2
Moments
.......................................................242
21.3
Computing Table Values
.......................................243
21.4
Maximum
Likelihood Estimators...............................
244
21.5
Applications
....................................................244
21.6
Properties and Results
.........................................245
21.7
Random Number Generation
...................................245
22 LOGNORMAL
DISTRIBUTION
22.1
Description
.....................................................247
22.2
Moments
.......................................................248
22.3
Computing Table Values
.......................................249
22.4
Maximum Likelihood Estimators
...............................250
22.5
Confidence Interval and Test for the Mean
......................250
22.6
Inferences for the Difference between Two Means
...............251
22.7
Inferences for the Ratio of Two Means
..........................253
22.8
Applications
...................................................254
22.9
Properties and Results
.........................................254
22.10
Random Number Generation
...................................255
22.11
Computation of Probabilities and Percentiles
...................255
23
PARETO DISTRIBUTION
23.1
Description
.....................................................257
23.2
Moments
.......................................................258
23.3
Computing Table Values
.......................................259
23.4
Inferences
......................................................259
23.4.1
Point Estimation
.......................................260
23.4.2
Interval Estimation
.....................................260
23.5
Applications
....................................................260
23.6
Properties and Results
.........................................261
23.7
Random Number Generation
...................................261
23.8
Computation of Probabilities and Percentiles
..................261
24
WEIBULL DISTRIBUTION
24.1
Description
.....................................................263
24.2
Moments
.......................................................264
24.3
Computing Table Values
.......................................265
24.4
Applications
....................................................265
24.5
Point Estimation
...............................................266
24.6
Properties and Results
.........................................267
24.7
Random Number Generation
...................................267
24.8
Computation of Probabilities and Percentiles
...................267
25
EXTREME VALUE DISTRIBUTION
25.1
Description
.....................................................269
25.2
Moments
.......................................................270
25.3
Computing Table Values
.......................................271
25.4
Maximum Likelihood Estimators
...............................271
25.5
Applications
....................................................272
25.6
Properties and Results
.........................................273
25.7
Random Number Generation
...................................273
25.8
Computation of Probabilities and Percentiles
...................273
26
CAUCHY DISTRIBUTION
26.1
Description
.....................................................275
26.2
Moments
.......................................................276
26.3
Computing Table Values
.......................................276
26.4
Inference
.......................................................277
26.4.1
Estimation Based on Sample Quantiles
.................277
26.4.2
Maximum Likelihood Estimators
.......................278
26.5
Applications
....................................................278
26.6
Properties and Results
.........................................278
26.7
Random Number Generation
...................................279
26.8
Computation of Probabilities and Percentiles
...................279
27
INVERSE
GAUSSIAN DISTRIBUTION
27.1
Description
.....................................................281
27.2
Moments
.......................................................282
27.3
Computing Table Values
.......................................283
27.4
One-Sample Inference
..........................................283
27.4.1
A Test for the Mean
....................................284
27.4.2
Confidence Interval for the Mean
.......................284
27.5
Two-Sample Inference
..........................................285
27.5.1
Inferences for the Difference between Two Means
.......285
27.5.2
Inferences for the Ratio of Two Means
..................287
27.6
Random Number Generation
...................................287
27.7
Computational Methods for Probabilities and Percentiles
......288
28
RAYLEIGH DISTRIBUTION
28.1
Description
.....................................................289
28.2
Moments
.......................................................290
28.3
Computing Table Values
.......................................290
28.4
Maximum Likelihood Estimator
................................291
28.5
Relation to Other Distributions
.................................291
28.6
Random Number Generation
...................................292
29
DIVARIATE
NORMAL DISTRIBUTION
29.1
Description
.....................................................293
29.2
Computing Table Values
.......................................294
29.3
An Example
....................................................295
29.4
Inferences on Correlation Coefficients
...........................296
29.4.1
Point Estimation
......................................297
29.4.2
Hypothesis Testing
....................................297
29.4.3
Interval Estimation
....................................299
29.4.4
Inferences on the Difference between Two
Correlation Coefficients
................................301
29.5
Some Properties
................................................303
29.6
Random Number Generation
...................................303
29.7
A Computational Algorithm for Probabilities
...................305
30 DISTRIBUTION
OF RUNS
30.1
Description
.....................................................307
30.2
Computing Table Values
.......................................309
30.3
Examples
......................................................309
31
SIGN TEST AND CONFIDENCE INTERVAL FOR
THE MEDIAN
31.1
Hypothesis Test for the Median
.................................311
31.2
Confidence Interval for the Median
.............................312
31.3
Computing Table Values
.......................................312
31.4
An Example
....................................................313
32
WILCOXON SIGNED-RANK TEST
32.1
Description
....................................................315
32.2
Moments and an Approximation
................................316
32.3
Computing Table Values
.......................................317
32.4
An Example
....................................................317
33
WILCOXON RANK-SUM TEST
33.1
Description
....................................................319
33.2
Moments and an Approximation
................................320
33.3
Mann-Whitney
U
Statistic
.....................................320
33.4
Computing Table Values
.......................................321
33.5
An Example
....................................................321
34
NONPARAMETRIC TOLERANCE INTERVAL
34.1
Description
....................................................323
34.2
Computing Table Values
.......................................324
34.3
An Example
....................................................324
35
TOLERANCE
FACTORS
FOR A MULTIVARIATE NORMAL
POPULATION
35.1
Description
.....................................................325
35.2
Computing Tolerance Factors
...................................326
35.3
Examples
......................................................326
36
DISTRIBUTION OF THE SAMPLE MULTIPLE
CORRELATION COEFFICIENT
36.1
Description
....................................................329
36.2
Moments
.......................................................330
36.3
Inferences
......................................................330
36.3.1
Point Estimation
.......................................330
36.3.2
Interval Estimation
.....................................331
36.3.3
Hypothesis Testing
.....................................331
36.4
Some Results
...................................................332
36.5
Random Number Generation
...................................332
36.6
A Computational Method for Probabilities
.....................332
36.7
Computing Table Values
.......................................334
REFERENCES
...........................................................335
INDEX
...................................................................345
The first reference of its kind, the Handbook of Statistical Distributions with
Applications combines popular probability distribution models, formulas,
applications, and software to assist in computing probabilities, percentiles,
moments, and other statistics.
Presenting both common and specialized probability distribution models as well
as providing applications with practical examples, this handbook offers
comprehensive coverage of plots of probability density functions, methods of
computing probability and percentiles, algorithms for random number generation,
and inference, including point estimation, hypothesis tests, and sample size
determination. Developed by the author, the StatCal software offers a useful
reference for computing distribution information, such as calculating probabilities,
parameters, and moments; finding exact tests; and obtaining exact confidence
intervals for binomial, hypergeometric,
Poisson,
negative binomial, normal,
lognormal,
and inverse Gaussian distributions.
In the applied statistics world, the Handbook of Statistical Distributions with
Applications is the definitive resource for examining distribution functions
—
including univariate, bivariate normal, and multivariate
—
their definitions, their
use in statistical inference, and their algorithms for random number generation.
Features
•
Explains various probability models and their applications with many illustrative,
practical examples
•
Includes a CD-ROM containing a simple PC calculator that computes
probabilities, percentiles, and other table values for roughly
34
statistical
distributions
•
Provides quick and easy access to table values, important formulas, and
results of statistical distributions
•
Gives recent solutions to problems that did not already have satisfactory
solutions available
•
Uses computational algorithms that have been tested for accuracy
|
| adam_txt |
Contents
INTRODUCTION
TO STATCALC
0.1
Introduction
.
0.2
Contents of StatCalc.
1
PRELIMINARIES
1.1
Random Variables and Expectations
.9
1.2
Moments and Other Functions
.12
1.2.1
Measures of Central Tendency
.12
1.2.2
Moments
.12
1.2.3
Measures of Variability
.13
1.2.4
Measures of Relative Standing
.14
1.2.5
Other Measures
.14
1.2.6
Some Other Functions
.15
1.3
Some Functions Relevant to Reliability
.15
1.4
Model Fitting
.16
1.4.1
Q-Q Plot
.17
1.4.2
The Chi-Square Goodness-of-Fit Test
.17
1.5
Methods of Estimation
.18
1.5.1
Moment Estimation
.18
1.5.2
Maximum Likelihood Estimation
.19
1.6
Inference
.19
1.6.1
Hypothesis Testing
.19
1.6.2
Interval Estimation
.23
1.7
Random Number Generation
.24
1.8
Some Special Functions
.25
2
DISCRETE UNIFORM
DISTRIBUTION
2.1
Description
.29
2.2
Moments
.
ЗО
3
BINOMIAL
DISTRIBUTION
3.1
Description
.31
3.2
Moments
.32
3.3
Computing Table Values
.34
3.4
Test for the
Proportion
.36
3.4.1
An Exact Test
.36
3.4.2
Power
of the
Exact Test
.36
3.5
Confidence
Intervals for the
Proportion
.38
3.5.1
An Exact Confidence
Interval
.38
3.5.2
Computing Exact
Limits and Sample Size Calculation
.39
3.6
A
Test for the Difference between Two Proportions
.40
3.6.1
An Unconditional Test
.40
3.6.2
Power of the Unconditional Test
.41
3.7
Fisher's Exact Test
.42
3.7.1
Calculation of p-Values
.43
3.7.2
Exact Powers
.44
3.8
Properties and Results
.45
3.8.1
Properties
.45
3.8.2
Relation to Other Distributions
.45
3.8.3
Approximations
.46
3.9
Random Number Generation
.46
3.10
Computation of Probabilities
.48
4
HYPERGEOMETRIC DISTRIBUTION
4.1
Description
.51
4.2
Moments
.52
4.3
Computing Table Values
.54
4.4
Point Estimation
.56
4.5
Test for the Proportion
.57
4.5.1
An Exact Test
.57
4.5.2
Power of the Exact Test
.58
4.6
Confidence Intervals and Sample Size Calculation
.59
4.6.1
Confidence Intervais
.59
4.6.2
Sample
Size for Precision
.60
4.7
A Test for the Difference between Two Proportions
.62
4.7.1
The Test
.62
4.7.2
Power Calculation
.63
4.8
Properties and Results
.64
4.8.1
Recurrence Relations
.64
4.8.2
Relation to Other Distributions
.64
4.8.3
Approximations
.64
4.9
Random Number Generation
.65
4.10
Computation of Probabilities
.66
5
POISSON
DISTRIBUTION
5.1
Description
.71
5.2
Moments
.72
5.3
Computing Table Values
.74
5.4
Point Estimation
.75
5.5
Test for the Mean
.75
5.5.1
An Exact Test
.75
5.5.2
Powers of the Exact Test
.76
5.6
Confidence Intervals for the Mean
.77
5.6.1
An Exact Confidence Interval
.77
5.6.2
Sample Size Calculation for Precision
.78
5.7
Test for the Ratio of Two Means
.78
5.7.1
A Conditional Test
.78
5.7.2
Powers of the Conditional Test
.80
5.8
Confidence Intervals for the Ratio of Two Means
.81
5.9
A Test for the Difference between Two Means
.81
5.9.1
An Unconditional Test
.82
5.9.2
Powers of the Unconditional Test
.83
5.10
Model Fitting with Examples
.84
5.11
Properties and Results
.86
5.11.1
Properties
.86
5.11.2
Relation to Other Distributions
.86
5.11.3
Approximations
.87
5.12
Random Number Generation
.87
5.13
Computation of Probabilities
.88
6
GEOMETRIC
DISTRIBUTION
6.1
Description
.93
6.2
Moments
.94
6.3
Computing Table Values
.94
6.4
Properties and Results
.95
6.5
Random Number Generation
.96
7
NEGATIVE BINOMIAL DISTRIBUTION
7.1
Description
.97
7.2
Moments
.98
7.3
Computing Table Values
.100
7.4
Point Estimation
.101
7.5
A Test for the Proportion
.101
7.6
Confidence Intervals for the Proportion
.103
7.7
Properties and Results
.103
7.7.1
Properties
.103
7.7.2
Relation to Other Distributions
.104
7.8
Random Number Generation
.104
7.9
A Computational Method for Probabilities
.106
8
LOGARITHMIC SERIES DISTRIBUTION
8.1
Description
.107
8.2
Moments
.109
8.3
Computing Table Values
.109
8.4
Inferences
.112
8.4.1
Point Estimation
.112
8.4.2
Interval Estimation
.112
8.5
Properties and Results
.113
8.6
Random Number Generation
.113
8.7
A Computational Algorithm for Probabilities
.114
9
UNIFORM DISTRIBUTION
9.1
Description
.115
9.2
Moments
.116
9.3
Inferences
.116
9.4
Properties and Results
.117
9.5
Random Number Generation
.117
10
NORMAL DISTRIBUTION
10.1
Description
.119
10.2
Moments
.123
10.3
Computing Table Values
.123
10.4
One-Sample Inference
.127
10.4.1
Point Estimation
.127
10.4.2
Test for the Mean and Power Computation
.128
10.4.3
Interval Estimation for the Mean
.130
10.4.4
Test and Interval Estimation for the Variance
.132
10.5
Two-Sample Inference
.134
10.5.1
Inference for the Ratio of Variances
.135
10.5.2
Inference for the Difference between Two Means
when the Variances Are Equal
.136
10.5.3
Inference for the Difference between Two Means
.140
10.6
Tolerance Intervals
.142
10.6.1
Two-Sided Tolerance Intervals
.142
10.6.2
One-Sided Tolerance Limits
.143
10.6.3
Equal-Tail Tolerance Intervals
.145
10.6.4
Simultaneous Hypothesis Testing for Quantiles
.146
10.6.5
Tolerance Limits for One-Way Random Effects Model.
. 147
10.7
Properties and Results
.149
10.8
Relation to Other Distributions
.150
10.9
Random Number Generation
.151
10.10
Computing the Distribution Function
.152
11
CHI-SQUARE DISTRIBUTION
11.1
Description
.155
11.2
Moments
.156
11.3
Computing Table Values
.157
11.4
Applications
.157
11.5
Properties and Results
.158
11.5.1
Properties
.158
11.5.2
Relation to Other Distributions
.159
11.5.3
Approximations
.160
11.6
Random Number Generation
.161
11.7
Computing the Distribution Function
.161
12
F DISTRIBUTION
12.1
Description
.163
12.2
Moments
.165
12.3
Computing Table Values
.165
12.4
Properties and Results
.166
12.4.1
Identities.
166
12.4.2
Relation
to Other
Distributions
.166
12.4.3
Series
Expansions
.167
12.4.4
Approximations
.168
12.5
Random Number Generation
.168
12.6
A Computational Method for Probabilities
.169
13
STUDENT'S
t
DISTRIBUTION
13.1
Description
.171
13.2
Moments
.172
13.3
Computing Table Values
.173
13.4
Distribution of the Maximum of Several |t| Variables
.173
13.4.1
An Application
.174
13.4.2
Computing Table Values
.175
13.4.3
An Example
.175
13.5
Properties and Results
.176
13.5.1
Properties
.176
13.5.2
Relation to Other Distributions
.176
13.5.3
Series Expansions for Cumulative Probability
.177
13.5.4
An Approximation
.178
13.6
Random Number Generation
.178
13.7
A Computational Method for Probabilities
.178
14
EXPONENTIAL DISTRIBUTION
14.1
Description
.179
14.2
Moments
.180
14.3
Computing Table Values
.180
14.4
Inferences
.181
14.5
Properties and Results
.182
14.5.1
Properties
.182
14.5.2
Relation to Other Distributions
.182
14.6
Random Number Generation
.183
15
GAMMA
DISTRIBUTION
15.1
Description
.185
15.2
Moments
. 186
15.3
Computing Table Values
.187
15.4
Applications
with Some Examples
.188
15.5
Inferences
.189
15.5.1
Maximum Likelihood Estimators
.189
15.5.2
Moment Estimators
.190
15.5.3
Interval Estimation
.190
15.6
Properties and Results
.191
15.7
Random Number Generation
.192
15.8
A Computational Method for Probabilities
.193
16
BETA DISTRIBUTION
16.1
Description
.195
16.2
Moments
.196
16.3
Computing Table Values
.197
16.4
Inferences
.198
16.5
Applications with an Example
.198
16.6
Properties and Results
.201
16.6.1
An Identity and Recurrence Relations
.201
16.6.2
Relation to Other Distributions
.202
16.7
Random Number Generation
.203
16.8
Evaluating the Distribution Function
.205
17
NONCENTRAL
CHI-SQUARE DISTRIBUTION
17.1
Description
.207
17.2
Moments
.209
17.3
Computing Table Values
.209
17.4
Applications
.210
17.5
Properties and Results
.211
17.5.1
Properties
.211
17.5.2
Approximations to Probabilities
.211
17.5.3
Approximations to Percentiles
.211
17.6
Random Number Generation
.212
17.7
Evaluating the Distribution Function
.212
18
NONCENTRAL F
DISTRIBUTION
18.1
Description
.217
18.2
Moments
.219
18.3
Computing Table Values
.219
18.4
Applications
.219
18.5
Properties and Results
.220
18.5.1
Properties.
220
18.5.2
Approximations
.221
18.6
Random Number Generation
.221
18.7
Evaluating the Distribution Function
.222
19
NONCENTRAL t
DISTRIBUTION
19.1
Description
.225
19.2
Moments
.226
19.3
Computing Table Values
.227
19.4
Applications
.227
19.5
Properties and Results
.228
19.5.1
Properties
.228
19.5.2
An Approximation
.229
19.6
Random Number Generation
.229
19.7
Evaluating the Distribution Function
.229
20
LAPLACE DISTRIBUTION
20.1
Description
.233
20.2
Moments
.234
20.3
Computing Table Values
.235
20.4
Inferences
.235
20.4.1
Maximum Likelihood Estimators
.235
20.4.2
Interval Estimation
.236
20.5
Applications
.236
20.6
Relation to Other Distributions
.238
20.7
Random Number Generation
.239
21
LOGISTIC
DISTRIBUTION
21.1
Description
.241
21.2
Moments
.242
21.3
Computing Table Values
.243
21.4
Maximum
Likelihood Estimators.
244
21.5
Applications
.244
21.6
Properties and Results
.245
21.7
Random Number Generation
.245
22 LOGNORMAL
DISTRIBUTION
22.1
Description
.247
22.2
Moments
.248
22.3
Computing Table Values
.249
22.4
Maximum Likelihood Estimators
.250
22.5
Confidence Interval and Test for the Mean
.250
22.6
Inferences for the Difference between Two Means
.251
22.7
Inferences for the Ratio of Two Means
.253
22.8
Applications
.254
22.9
Properties and Results
.254
22.10
Random Number Generation
.255
22.11
Computation of Probabilities and Percentiles
.255
23
PARETO DISTRIBUTION
23.1
Description
.257
23.2
Moments
.258
23.3
Computing Table Values
.259
23.4
Inferences
.259
23.4.1
Point Estimation
.260
23.4.2
Interval Estimation
.260
23.5
Applications
.260
23.6
Properties and Results
.261
23.7
Random Number Generation
.261
23.8
Computation of Probabilities and Percentiles
.261
24
WEIBULL DISTRIBUTION
24.1
Description
.263
24.2
Moments
.264
24.3
Computing Table Values
.265
24.4
Applications
.265
24.5
Point Estimation
.266
24.6
Properties and Results
.267
24.7
Random Number Generation
.267
24.8
Computation of Probabilities and Percentiles
.267
25
EXTREME VALUE DISTRIBUTION
25.1
Description
.269
25.2
Moments
.270
25.3
Computing Table Values
.271
25.4
Maximum Likelihood Estimators
.271
25.5
Applications
.272
25.6
Properties and Results
.273
25.7
Random Number Generation
.273
25.8
Computation of Probabilities and Percentiles
.273
26
CAUCHY DISTRIBUTION
26.1
Description
.275
26.2
Moments
.276
26.3
Computing Table Values
.276
26.4
Inference
.277
26.4.1
Estimation Based on Sample Quantiles
.277
26.4.2
Maximum Likelihood Estimators
.278
26.5
Applications
.278
26.6
Properties and Results
.278
26.7
Random Number Generation
.279
26.8
Computation of Probabilities and Percentiles
.279
27
INVERSE
GAUSSIAN DISTRIBUTION
27.1
Description
.281
27.2
Moments
.282
27.3
Computing Table Values
.283
27.4
One-Sample Inference
.283
27.4.1
A Test for the Mean
.284
27.4.2
Confidence Interval for the Mean
.284
27.5
Two-Sample Inference
.285
27.5.1
Inferences for the Difference between Two Means
.285
27.5.2
Inferences for the Ratio of Two Means
.287
27.6
Random Number Generation
.287
27.7
Computational Methods for Probabilities and Percentiles
.288
28
RAYLEIGH DISTRIBUTION
28.1
Description
.289
28.2
Moments
.290
28.3
Computing Table Values
.290
28.4
Maximum Likelihood Estimator
.291
28.5
Relation to Other Distributions
.291
28.6
Random Number Generation
.292
29
DIVARIATE
NORMAL DISTRIBUTION
29.1
Description
.293
29.2
Computing Table Values
.294
29.3
An Example
.295
29.4
Inferences on Correlation Coefficients
.296
29.4.1
Point Estimation
.297
29.4.2
Hypothesis Testing
.297
29.4.3
Interval Estimation
.299
29.4.4
Inferences on the Difference between Two
Correlation Coefficients
.301
29.5
Some Properties
.303
29.6
Random Number Generation
.303
29.7
A Computational Algorithm for Probabilities
.305
30 DISTRIBUTION
OF RUNS
30.1
Description
.307
30.2
Computing Table Values
.309
30.3
Examples
.309
31
SIGN TEST AND CONFIDENCE INTERVAL FOR
THE MEDIAN
31.1
Hypothesis Test for the Median
.311
31.2
Confidence Interval for the Median
.312
31.3
Computing Table Values
.312
31.4
An Example
.313
32
WILCOXON SIGNED-RANK TEST
32.1
Description
.315
32.2
Moments and an Approximation
.316
32.3
Computing Table Values
.317
32.4
An Example
.317
33
WILCOXON RANK-SUM TEST
33.1
Description
.319
33.2
Moments and an Approximation
.320
33.3
Mann-Whitney
U
Statistic
.320
33.4
Computing Table Values
.321
33.5
An Example
.321
34
NONPARAMETRIC TOLERANCE INTERVAL
34.1
Description
.323
34.2
Computing Table Values
.324
34.3
An Example
.324
35
TOLERANCE
FACTORS
FOR A MULTIVARIATE NORMAL
POPULATION
35.1
Description
.325
35.2
Computing Tolerance Factors
.326
35.3
Examples
.326
36
DISTRIBUTION OF THE SAMPLE MULTIPLE
CORRELATION COEFFICIENT
36.1
Description
.329
36.2
Moments
.330
36.3
Inferences
.330
36.3.1
Point Estimation
.330
36.3.2
Interval Estimation
.331
36.3.3
Hypothesis Testing
.331
36.4
Some Results
.332
36.5
Random Number Generation
.332
36.6
A Computational Method for Probabilities
.332
36.7
Computing Table Values
.334
REFERENCES
.335
INDEX
.345
The first reference of its kind, the Handbook of Statistical Distributions with
Applications combines popular probability distribution models, formulas,
applications, and software to assist in computing probabilities, percentiles,
moments, and other statistics.
Presenting both common and specialized probability distribution models as well
as providing applications with practical examples, this handbook offers
comprehensive coverage of plots of probability density functions, methods of
computing probability and percentiles, algorithms for random number generation,
and inference, including point estimation, hypothesis tests, and sample size
determination. Developed by the author, the StatCal software offers a useful
reference for computing distribution information, such as calculating probabilities,
parameters, and moments; finding exact tests; and obtaining exact confidence
intervals for binomial, hypergeometric,
Poisson,
negative binomial, normal,
lognormal,
and inverse Gaussian distributions.
In the applied statistics world, the Handbook of Statistical Distributions with
Applications is the definitive resource for examining distribution functions
—
including univariate, bivariate normal, and multivariate
—
their definitions, their
use in statistical inference, and their algorithms for random number generation.
Features
•
Explains various probability models and their applications with many illustrative,
practical examples
•
Includes a CD-ROM containing a simple PC calculator that computes
probabilities, percentiles, and other table values for roughly
34
statistical
distributions
•
Provides quick and easy access to table values, important formulas, and
results of statistical distributions
•
Gives recent solutions to problems that did not already have satisfactory
solutions available
•
Uses computational algorithms that have been tested for accuracy |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Krishnamoorthy, Kalimuthu 1955- |
| author_GND | (DE-588)1063111919 |
| author_facet | Krishnamoorthy, Kalimuthu 1955- |
| author_role | aut |
| author_sort | Krishnamoorthy, Kalimuthu 1955- |
| author_variant | k k kk |
| building | Verbundindex |
| bvnumber | BV022889872 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.6 |
| callnumber-search | QA273.6 |
| callnumber-sort | QA 3273.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 |
| ctrlnum | (OCoLC)64688916 (DE-599)BVBBV022889872 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV022889872 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:53:12Z |
| indexdate | 2024-07-09T21:07:50Z |
| institution | BVB |
| isbn | 1584886358 9781584886358 |
| language | English |
| lccn | 2006040297 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016094760 |
| oclc_num | 64688916 |
| open_access_boolean | |
| owner | DE-739 DE-M347 DE-578 |
| owner_facet | DE-739 DE-M347 DE-578 |
| physical | 346 S. Ill. 24 cm. + 1 CD-ROM, 12 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Statistics |
| series2 | Statistics |
| spelling | Krishnamoorthy, Kalimuthu 1955- Verfasser (DE-588)1063111919 aut Handbook of statistical distributions with applications K. Krishnamoorthy Boca Raton [u.a.] Chapman & Hall/CRC 2006 346 S. Ill. 24 cm. + 1 CD-ROM, 12 cm txt rdacontent n rdamedia nc rdacarrier Statistics 188 Includes bibliographical references and index Distribution (Théorie des probabilités) - Guides, manuels, etc Verdelingen (statistiek) gtt Distribution (Probability theory) Handbooks, manuals, etc Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Statistics 188 (DE-604)BV000003265 188 http://www.loc.gov/catdir/enhancements/fy0654/2006040297-d.html Publisher description Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016094760&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016094760&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Krishnamoorthy, Kalimuthu 1955- Handbook of statistical distributions with applications Statistics Distribution (Théorie des probabilités) - Guides, manuels, etc Verdelingen (statistiek) gtt Distribution (Probability theory) Handbooks, manuals, etc Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4121894-2 |
| title | Handbook of statistical distributions with applications |
| title_auth | Handbook of statistical distributions with applications |
| title_exact_search | Handbook of statistical distributions with applications |
| title_exact_search_txtP | Handbook of statistical distributions with applications |
| title_full | Handbook of statistical distributions with applications K. Krishnamoorthy |
| title_fullStr | Handbook of statistical distributions with applications K. Krishnamoorthy |
| title_full_unstemmed | Handbook of statistical distributions with applications K. Krishnamoorthy |
| title_short | Handbook of statistical distributions with applications |
| title_sort | handbook of statistical distributions with applications |
| topic | Distribution (Théorie des probabilités) - Guides, manuels, etc Verdelingen (statistiek) gtt Distribution (Probability theory) Handbooks, manuals, etc Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Distribution (Théorie des probabilités) - Guides, manuels, etc Verdelingen (statistiek) Distribution (Probability theory) Handbooks, manuals, etc Wahrscheinlichkeitsverteilung |
| url | http://www.loc.gov/catdir/enhancements/fy0654/2006040297-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016094760&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016094760&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003265 |
| work_keys_str_mv | AT krishnamoorthykalimuthu handbookofstatisticaldistributionswithapplications |