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Larsen R.J., Marx M.L. — Introduction to Mathematical Statistics and Its Applications, An (4th Edition)
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Íàçâàíèå: Introduction to Mathematical Statistics and Its Applications, An (4th Edition)Àâòîðû: Larsen R.J., Marx M.L. Àííîòàöèÿ: 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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Èçäàíèå: 4Ãîä èçäàíèÿ: 2005Êîëè÷åñòâî ñòðàíèö: 928Äîáàâëåíà â êàòàëîã: 02.10.2015Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Normal distribution, in linear model 678—679 Normal distribution, independence of sample mean and sample variance 474 514—516 Normal distribution, moment-generating function 260 311 Normal distribution, Moments 308 Normal distribution, parameter estimation 353—354 383—384 Normal distribution, relationship to chi square distribution 474 476 Normal distribution, table 294—297 851—852 Normal distribution, transformation to standard normal 267—268 308 Normal distribution, unbiased estimator for variance 383—384 683—684 Null hypothesis 428 436 One-sample data 435 440 483 490 501 504 528—529 804 One-sample t test 489—490 513—514 Operating characteristic curve 146 Order statistics, definition 241 Order statistics, estimates based on 350—351 Order statistics, joint pdf 246—247 Order statistics, probability density function for ith 242—244 Outliers 640—642 p-value 437—438 Paired data 532 788 807—808 820—822 Paired t test 789—793 796—800 pairwise comparisons see "Tukey’s test" Palindrome 103—104 PARAMETER 344 Parameter space 463—465 Pareto distribution 356 Partitioned sample space 56—57 63 410—411 Pascal’s triangle 110 Pearson product moment correlation coefficient 709 Permutations objects all distinct 93 Permutations objects not all distinct 100 Poisson distribution, additive property 267 Poisson distribution, approximated by normal distribution 305—306 Poisson distribution, as limit of binomial distribution 276—277 Poisson distribution, definition 281 Poisson distribution, hypothesis test 457—458 Poisson distribution, moment-generating function 265 Poisson distribution, Moments 265 281 Poisson distribution, parameter estimation 352—353 402 411—412 422 Poisson distribution, relationship to exponential distribution 289—290 Poisson distribution, relationship to gamma distribution 327 415 Poisson distribution, square root transformation 759 Poisson model 284—285 Poker hands 119—121 Political arithmetic 7—10 Posterior distribution 412—416 Power 449—454 771 Power curve 450 466—468 Prediction interval 695—696 Prior distribution 411—416 Probability density function (pdf) 155 168—169 215 220 223—225 Probability function 36—38 149 161—163 Probability, axiomatic definition 23 36—38 Probability, classical definition 6 22 113 Probability, empirical definition 22—23 125—127 Problem of points 7 Producer’s risk 459 Propagation of errors 237—240 Qualitative measurement 525—527 Quantitative measurement 525—526 Random Mendelian mating 73 Random sample 219 Random variable 129 149 154 168—169 Randomized block data 532—534 773—774 Randomized block design, block sum of squares 776 Randomized block design, comparison with completely randomized one-factor design 780 Randomized block design, computing formulas 778 Randomized block design, error sum of squares 775—776 Randomized block design, notation 774 Randomized block design, relationship to paired t test 794—795 Randomized block design, test statistic 111 Randomized block design, treatment sum of squares 776 RANGE 247—248 Rank sum test see "Wilcoxon rank sum test" Rayleigh distribution 181—182 Rectangular distribution see "Uniform distribution" Regression curve 677—679 720 Regression data 534—535 647 677—679 702 Relative efficiency 388—393 Repeated independent trials 78 Residual 650 Residual plot 650—655 Risk 420—422 Robustness 485 493—498 560 623 803 841—846 runs 835—838 Sample correlation coefficient, definition 709—710 Sample correlation coefficient, in tests of independence 721—723 Sample correlation coefficient, interpretation and misinterpretation 709—714 725 Sample outcome 24 Sample size determination 373—374 454—455 552 Sample space 24 56—57 Sample standard deviation 384 Sample variance 384 555 683—684 697 737 776 Sampling plan 145—146 Serial number analysis 391—393 Sign test 804—808 846 Signed rank test see "Wilcoxon signed rank test" skewness 200 Spurious correlation 725 Square root transformation 759 Squared-error consistent 409 St. Petersburg paradox 180—181 Standard deviation 195 384 Standard normal distribution, definition 294 Standard normal distribution, in central limit theorem 302 307 Standard normal distribution, in de Moivre — Laplace limit theorem 293 Standard normal distribution, table 294—296 851—852 Standard normal distribution, Z transformation 267—268 308 312 Statistic 346 Statistically significant 433 Stirling’s formula 96 102 Student t distribution, approximated by standard normal distribution 470—472 478—479 Student t distribution, definition 476—478 Student t distribution, in inferences about difference between two dependent means 789 Student t distribution, in inferences about difference between two independent means 519—521 555 557 563 567 Student t distribution, in inferences about single mean 482—483 489—490 Student t distribution, in regression analysis 684—685 688 690 694 696—697 722 Student t distribution, moments 201—202 Student t distribution, relationship to chi square distribution 476 Student t distribution, relationship to F distribution 476—477 Student t distribution, table 481—482 853—855 Studentized range 748 872—873 Subhypothesis 747—748 751—754 Sufficient estimator, definition 398 401—402 Sufficient estimator, examples 398—400 Sufficient estimator, exponential form 405 Sufficient estimator, factorization criterion 403 Sufficient estimator, relationship to maximum likelihood estimator 404 Sufficient estimator, relationship to minimum variance, unbiased estimator 405 Test statistic 433 Testing, a single mean with variance known 435 Testing, a single mean with variance unknown 490 519—521 Testing, a single median 804 Testing, a single proportion 440 Testing, a single variance 504 516—519 Testing, for goodness-of-fit 606—607 616 642—644 Testing, for independence 627—631 685 Testing, for randomness 836 Testing, subhypotheses 747—748 754 Testing, that correlation coefficient is zero 720—721 723 Testing, the equality of k location parameters (dependent samples) 832 Testing, the equality of k location parameters (independent samples) 826—827 Testing, the equality of k means (dependent samples) 777 Testing, the equality of k means (independent samples) 737—739 Testing, the equality of two location parameters (dependent samples) 807 Testing, the equality of two location parameters (independent samples) 822—823 Testing, the equality of two means (dependent samples) 789 Testing, the equality of two means (independent samples) 557 563 567 Testing, the equality of two proportions (independent samples) 578 Testing, the equality of two slopes (independent samples) 697 Testing, the equality of two variances (independent samples) 569 Testing, the parameter of Poisson distribution 457—458 Testing, the parameter of uniform distribution 462—465 Testing, the slope of a regression line 685 Threshold parameter 351 Treatment 523—524 Treatment sum of squares 735—738 754 766—767 776 Trinomial distribution 605 Tukey’s test 747—750 781—782 Two-sample data 529—530 554—555 569 578 582 585 587 822 Two-sample t test 554 557 697 745—746 796—800 Type I error 447—448 457—458 747 Type II error 447—459 Unbiased estimator 381—385 Uniform distribution 163—164 207—209 304—305 382—383 390—391 462—465 union 28 Variance see also "Sample variance" Variance, computing formula 195 Variance, confidence interval 501 Variance, definition 194 Variance, in hypothesis tests 504 569 Variance, lower bound (Cramer — Rao) 394 Variance, of a function 237—240 Variance, of a sum 234—236 705 753 Variance, properties 197 Venn diagrams 33—35 39 45—46 Weak law of large numbers 409 Wilcoxon rank sum test 822—824 Wilcoxon signed rank test 810—822 847 874—875
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