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Larsen R.J., Marx M.L. Ч Introduction to Mathematical Statistics and Its Applications, An (4th Edition)
Larsen R.J., Marx M.L. Ч Introduction to Mathematical Statistics and Its Applications, An (4th Edition)

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Ќазвание: Introduction to Mathematical Statistics and Its Applications, An (4th Edition)

јвторы: Larsen R.J., Marx M.L.


I am surprised by the number of negative reviews for what I consider to be a nicely written, well thought out, and logically presented introductory course on mathematical statistics. Yes, a working knowledge of elementary calculus is a prerequisite. But the mathematics invoked in the exposition of concepts and theorems are kept as simple as possible while maintaining that modest level of rigor appropriate for a introductory exposition. If you do not have the minimal mathematical prerequisites (such as freshman calculus), blame your instructor or your school for selecting an inappropriate text. But don't blame the authors! I thought the examples and problems were appropriate in their level of difficulty (mostly not so hard) and the relation to the material just covered. There are plenty of poorly written, impossibly dry, inpenetrable texts on statistics out there - this is not one of them. In addition, the book is attractively packaged, the paper quality is excellent, the visuals are informative and clearly presented - that also should not be taken for granted. Lastly the authors have a wicked entertaining sense of humor that spice the presentation throughout. I consider this book to be a welcome addition to the set of modern textbooks available to the curious serious student of probability and statistics.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 4

√од издани€: 2005

 оличество страниц: 928

ƒобавлена в каталог: 02.10.2015

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ѕредметный указатель
Alternative hypothesis      428 434Ч435
ANOVA table      739Ч740 763 111
Arc sine transformation      759Ч760
Asymptotically unbiased      388 406
Bayes theorem      62Ч63 79Ч81 410Ч411
Bayesian estimation      410Ч422
Behrens Ч Fisher problem      555 567
Benford's law      152Ч153 609Ч611
Bernoulli distribution      229 235 344Ч346 394Ч395
Bernoulli trials      229
Bertillon configuration      87
Best estimator      395
Beta distribution      413
Bills of mortality      8Ч10
Binomial coefficients      108 110Ч113
Binomial distribution, additive property      221Ч222
Binomial distribution, arc sine transformation      759Ч760
Binomial distribution, confidence interval for p      369Ч371 587Ч588
Binomial distribution, definition      131 155
Binomial distribution, estimate for p      344Ч346 380Ч381 394Ч395
Binomial distribution, hypothesis tests for p      440 443Ч445 578Ч580
Binomial distribution, in sign test      804
Binomial distribution, moment-generating function      258Ч259
Binomial distribution, Moments      176 229 235 264Ч265
Binomial distribution, normal approximation      292Ч293 297Ч299 338Ч339
Binomial distribution, Poisson approximation      276Ч277
Binomial distribution, relationship to Bernoulli distribution      229 235
Binomial distribution, relationship to beta distribution      415
Binomial distribution, relationship to hypergeometric distribution      138Ч139
Binomial distribution, relationship to multinomial distribution      602Ч603
Binomial distribution, sample size determination      373Ч374
Birthday problem      117Ч119
Bivariate distribution      see "Joint probability density function"
Bivariate normal distribution      719Ч723
BLOCKS      524 773Ч774 788Ч789 792Ч793 796Ч800 832Ч833
categorical data      535Ч537 627Ч637
Central limit theorem      292Ч294 302Ч307
ChebyshevТs inequality      408Ч409
Chi square distribution, additive property      330
Chi square distribution, definition      474
Chi square distribution, formula for approximating percentiles      506Ч507
Chi square distribution, moment-generating function      332
Chi square distribution, moments      330
Chi square distribution, noncentral      767Ч769
Chi square distribution, relationship to F distribution      475
Chi square distribution, relationship to gamma distribution      474
Chi square distribution, relationship to normal distribution      474
Chi square distribution, relationship to Student t distribution      476
Chi square distribution, table      500Ч501 856Ч857
Chi square test for goodness-of-fit      599 606Ч607 616 642Ч644
Chi square test for independence      631
Chi square test for the variance      504 516Ч519
Chi square test in nonparametric analyses      827 832
Combinations      107
Complement      30
Completely randomized one-factor design comparison, with randomized block design      780
Completely randomized one-factor design, comparison with Kruskal Ч Wallis test      841Ч846
Completely randomized one-factor design, computing formulas      742
Completely randomized one-factor design, error sum of squares      737Ч738
Completely randomized one-factor design, notation      733Ч734
Completely randomized one-factor design, relationship to two-sample data      745Ч746
Completely randomized one-factor design, test statistic      738Ч739 769
Completely randomized one-factor design, total sum of squares      737Ч738
Completely randomized one-factor design, treatment sum of squares      735Ч738 754 766Ч767
Conditional expectation      677Ч679
Conditional probability definition      43Ч44 250
Conditional probability in bivariate distribution      249Ч256
Conditional probability in higher-order interactions      53Ч54
Conditional probability in partitioned sample spaces      56Ч57 62Ч63 410Ч411
Conditional probability in regression      677Ч679
Confidence band      695
Confidence coefficient      368Ч369
Confidence interval      see also "Prediction interval"
Confidence interval, definition      363Ч364
Confidence interval, for conditional mean in linear model      694
Confidence interval, for difference of two means      582
Confidence interval, for difference of two proportions      587
Confidence interval, for mean of normal distribution      364Ч369 481Ч482
Confidence interval, for p in binomial distribution      369Ч371
Confidence interval, for quotient of two variances      585
Confidence interval, for regression coefficients      688 690Ч691
Confidence interval, for variance of normal distribution      501
Confidence interval, interpretation      365Ч367 423Ч424
Confidence interval, relationship to hypothesis testing      585
Consistent estimator      406Ч409
ConsumerТs risk      459
Contingency table      536 628 635
Continuity correction      296Ч297
contrast      751Ч756 782Ч784
Correlation coefficient, applied to linear relationships      707
Correlation coefficient, definition      707
Correlation coefficient, estimate      708Ч709
Correlation coefficient, in bivariate normal distribution      719Ч723
Correlation coefficient, interpretation      710 719
Correlation coefficient, relationship to covariance      707
Correlation coefficient, relationship to independence      704
Covariance      702Ч705 707
Cramer Ч Rao lower bound      394Ч397 404Ч405
Critical region      433
Critical value      433
Cumulative distribution function (cdf), definition      159 170 213
Cumulative distribution function (cdf), in pdf of order statistics      244 247
Cumulative distribution function (cdf), relationship to pdf      170 214
Curve-fitting, examples      648Ч655 663Ч671
Curve-fitting, method of least squares      647Ч648
Curve-fitting, residual      650
Curve-fitting, residual plot      650Ч655
Curve-fitting, transformations to induce linearity      662Ч663 666 668Ч669 671
Data transformations      758Ч760
De Moivre Ч Laplace limit theorem      292Ч293 301Ч302
de MorganТs laws      35
Density function      see "Probability density function (pdf)"
Density-scaled histogram      165Ч168 291 339Ч340 359Ч362
Dependent samples      524Ч525 773Ч774 792Ч793 796Ч800
Distribution-free statistics      see "Nonparametric statistics"
Efficiency      388Ч393 396
Efficient estimator      395Ч396
Estimation      see also "Confidence interval"
Estimation, Bayesian      410Ч422
Estimation, least squares      647Ч648
Estimation, maximum likelihood      344Ч354
Estimation, method of moments      357Ч362
Estimation, point versus interval      363Ч364
Estimator      see also "Confidence interval"
Estimator, best      396
Estimator, consistent      408Ч409
Estimator, Cramer Ч Rao lower bound      394
Estimator, difference between estimate and estimator      346 349
Estimator, efficient      396
Estimator, for binomial p      344Ч346 380Ч381 394Ч395
Estimator, for bivariate normal parameters      721
Estimator, for contrast      752Ч753
Estimator, for correlation coefficient      708Ч709
Estimator, for exponential parameter      351 385Ч386
Estimator, for gamma parameters      359Ч362
Estimator, for geometric parameter      348Ч349
Estimator, for normal parameters      353Ч354 383Ч384
Estimator, for Poisson parameter      352Ч353 402 411Ч412 422
Estimator, for slope and gamma-intercept (linear model)      679Ч681
Estimator, for uniform parameter      382Ч383 390Ч391 403 407 424Ч426
Estimator, for variance in linear model      683Ч684
Estimator, interval      363Ч364
Estimator, sufficient      398 401Ч402
Estimator, unbiasedness      381Ч385
Event      24
Expected value, conditional      677Ч679
Expected value, definition      175 199Ч201
Expected value, examples      174Ч182 227Ч228
Expected value, in method of moments estimation      357Ч358
Expected value, of functions      186Ч187 226Ч227 232Ч233 320Ч321
Expected value, of linear combinations      229
Expected value, of loss functions      420
Expected value, of sums      229Ч232
Expected value, relationship to median      182Ч183
Expected value, relationship to moment-generating function      261
Experiment      24
Experimental design      523 527Ч528 538Ч540 733 773Ч774 780 792Ч793 796Ч800
Exponential distribution, examples      161Ч163 167Ч168 183 222Ч223 242Ч243 290Ч292 333Ч337 351
Exponential distribution, memoryless property      256
Exponential distribution, moment-generating function      259
Exponential distribution, Moments      263
Exponential distribution, parameter estimation      351 385Ч386
Exponential distribution, relationship to Poisson distribution      289Ч290
Exponential distribution, threshold parameter      351
Exponential form      405
Exponential regression      662Ч666
F distribution, definition      475
F distribution, in analysis of variance      738Ч739 754Ч755 777
F distribution, in inferences about variance ratios      569 585
F distribution, relationship to chi square distribution      475
F distribution, relationship to Student t distribution      476Ч477
F distribution, table      476 857Ч871
Factorization theorem      403
Finite correction factor      375
FisherТs lemma      516
FriedmanТs test      832Ч833 848Ч849
Gamma distribution, additive property      330
Gamma distribution, definition      327 329
Gamma distribution, examples      328Ч329 331 359Ч362
Gamma distribution, moment-generating function      332
Gamma distribution, Moments      330
Gamma distribution, parameter estimation      359Ч362
Gamma distribution, relationship to chi square distribution      474
Gamma distribution, relationship to exponential distribution      327
Gamma distribution, relationship to normal distribution      474
Gamma distribution, relationship to Poisson distribution      327 415
Generalized likelihood ratio      463
Generalized likelihood ratio test (GLRT), definition      464
Generalized likelihood ratio test (GLRT), examples      464Ч465 516Ч521 569 577 593Ч595 607Ч608 735
Geometric distribution, definition      317Ч318
Geometric distribution, examples      317Ч321
Geometric distribution, memoryless property      319Ч320
Geometric distribution, moment-generating function      258 318
Geometric distribution, Moments      262 318
Geometric distribution, parameter estimation      348Ч349
Geometric distribution, relationship to negative binomial distribution      322
Geometric mean      385Ч386
Geometric probability      207Ч209
Hazard rate      173
Hypergeometric distribution, definition      139 155
Hypergeometric distribution, examples      141Ч146
Hypergeometric distribution, Moments      177 375 706
Hypergeometric distribution, relationship to binomial distribution      138Ч139
Hypothesis testing, critical region      433
Hypothesis testing, decision rule      428Ч432 455Ч459
Hypothesis testing, level of significance      434
Hypothesis testing, P-value      437Ч438
Hypothesis testing, Type I and Type II errors      447Ч459 747
Independence, effect of, on the expected value of a product      233
Independence, mutual versus pairwise      75Ч76
Independence, of events      44 70Ч72 75Ч77 627Ч630
Independence, of random variables      216 218
Independence, of regression estimators      683 728Ч731
Independence, of repeated trials      78Ч83
Independence, of sample mean and sample variance (normal data)      474 514Ч516
Independence, of sums of squares      737
Independence, tests for      627Ч631
Independent samples      524Ч525 529Ч532 554 733 796Ч800 822 826
Intersection      28
Interval estimate      see "Prediction interval"
Joint cumulative distribution function      213Ч215
Joint probability density function      203Ч207 215
k-sample data      531Ч532 733Ч734 826Ч827
Kruskal Ч Wallis test      826Ч830 841Ч848
kurtosis      200Ч201
Law of small numbers      284Ч285
level of significance      434 437 447Ч448 457Ч458 747
Likelihood function      347
Likelihood ratio      see "Generalized likelihood ratio"
Linear model, assumptions      677Ч679
Linear model, confidence intervals for parameters      688 690Ч691
Linear model, hypothesis tests      685 690Ч691 697
Linear model, parameter estimation      678Ч679 683Ч684
Logarithmic regression      666Ч668
Logistic regression      668Ч669
Loss function      419Ч422
Margin of error      372 423Ч424
Marginal probability density function      205 211Ч212 417
Maximum Likelihood Estimation      see also "Estimation"
Maximum likelihood, estimation definition      347
Maximum likelihood, estimation examples      344Ч346 348Ч354 679
Maximum likelihood, estimation in goodness-of-fit testing      615Ч616
Maximum likelihood, estimation in regression analysis      679 683Ч684
Maximum likelihood, estimation properties      404Ч405 409
Mean free path      181
Mean square      740
Median      182Ч183 388 804
Median unbiased      388
Method of least squares      see "Estimation"
Method of moments      see "Estimation"
Minimum variance estimator      395
MINITAB calculations for cdf      272Ч273 337Ч338
MINITAB calculations for completely randomized one-factor design      762Ч764
MINITAB calculations for confidence intervals      366 512Ч513 596Ч597
MINITAB calculations for critical values      512
MINITAB calculations for FriedmanТs test      848Ч849
MINITAB calculations for histograms      339Ч340
MINITAB calculations for independence      644Ч645 726Ч727
MINITAB calculations for Kruskal Ч Wallis test      847Ч848
MINITAB calculations for Monte Carlo analysis      333Ч339 366 385Ч386 424Ч426 432
MINITAB calculations for one-sample t test      513Ч514
MINITAB calculations for pdf      272 337 444
MINITAB calculations for randomized block design      800Ч801
MINITAB calculations for regression analysis      726Ч728
MINITAB calculations for robustness      495Ч498
MINITAB calculations for sample statistics      510Ч511
MINITAB calculations for Tukey confidence intervals      764Ч766
MINITAB calculations for two-sample t test      595Ч597
Model equation      529Ч537
Moment-generating function, as technique for finding distributions of sums      267
Moment-generating function, definition      257
Moment-generating function, examples      258Ч260 311
Moment-generating function, in proof of central limit theorem      341Ч342
Moment-generating function, properties      261 266
Moment-generating function, relationship to moments      261
Moments      see "Variance"
MooreТs Law      663Ч666
Multinomial coefficients      101
Multinomial distribution      600Ч603 607
Multiple comparisons      747Ч750
Multiplication rule      86
Mutually exclusive events      29 71
Negative binomial distribution      157 322Ч326
Noncentral chi square distribution      767
Noncentral F distribution      768Ч769
Noninformative prior      412
Nonparametric statistics      803
Normal distribution, additive property      312
Normal distribution, approximation to Binomial distribution      292Ч293 297Ч299 338Ч339
Normal distribution, approximation to Poisson distribution      305Ч306
Normal distribution, approximation to sign test      804
Normal distribution, approximation to Wilcoxon signed rank statistic      817
Normal distribution, as limit for Student t distribution      470Ч472 478Ч479
Normal distribution, central limit theorem      302 341Ч342
Normal distribution, confidence interval for mean      364Ч369 482Ч485 582Ч585
Normal distribution, confidence interval for variance      501Ч504
Normal distribution, definition      308
Normal distribution, hypothesis test for mean (variance known)      435
Normal distribution, hypothesis test for mean (variance unknown)      490 493Ч498
Normal distribution, hypothesis test for variance      504
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