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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 |
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Alternative hypothesis 428 434—435 ANOVA table 739—740 763 111 Arc sine transformation 759—760 Asymptotically unbiased 388 406 Bayes theorem 62—63 79—81 410—411 Bayesian estimation 410—422 Behrens — Fisher problem 555 567 Benford's law 152—153 609—611 Bernoulli distribution 229 235 344—346 394—395 Bernoulli trials 229 Bertillon configuration 87 Best estimator 395 Beta distribution 413 Bills of mortality 8—10 Binomial coefficients 108 110—113 Binomial distribution, additive property 221—222 Binomial distribution, arc sine transformation 759—760 Binomial distribution, confidence interval for p 369—371 587—588 Binomial distribution, definition 131 155 Binomial distribution, estimate for p 344—346 380—381 394—395 Binomial distribution, hypothesis tests for p 440 443—445 578—580 Binomial distribution, in sign test 804 Binomial distribution, moment-generating function 258—259 Binomial distribution, Moments 176 229 235 264—265 Binomial distribution, normal approximation 292—293 297—299 338—339 Binomial distribution, Poisson approximation 276—277 Binomial distribution, relationship to Bernoulli distribution 229 235 Binomial distribution, relationship to beta distribution 415 Binomial distribution, relationship to hypergeometric distribution 138—139 Binomial distribution, relationship to multinomial distribution 602—603 Binomial distribution, sample size determination 373—374 Birthday problem 117—119 Bivariate distribution see "Joint probability density function" Bivariate normal distribution 719—723 BLOCKS 524 773—774 788—789 792—793 796—800 832—833 categorical data 535—537 627—637 Central limit theorem 292—294 302—307 Chebyshev’s inequality 408—409 Chi square distribution, additive property 330 Chi square distribution, definition 474 Chi square distribution, formula for approximating percentiles 506—507 Chi square distribution, moment-generating function 332 Chi square distribution, moments 330 Chi square distribution, noncentral 767—769 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 500—501 856—857 Chi square test for goodness-of-fit 599 606—607 616 642—644 Chi square test for independence 631 Chi square test for the variance 504 516—519 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 — Wallis test 841—846 Completely randomized one-factor design, computing formulas 742 Completely randomized one-factor design, error sum of squares 737—738 Completely randomized one-factor design, notation 733—734 Completely randomized one-factor design, relationship to two-sample data 745—746 Completely randomized one-factor design, test statistic 738—739 769 Completely randomized one-factor design, total sum of squares 737—738 Completely randomized one-factor design, treatment sum of squares 735—738 754 766—767 Conditional expectation 677—679 Conditional probability definition 43—44 250 Conditional probability in bivariate distribution 249—256 Conditional probability in higher-order interactions 53—54 Conditional probability in partitioned sample spaces 56—57 62—63 410—411 Conditional probability in regression 677—679 Confidence band 695 Confidence coefficient 368—369 Confidence interval see also "Prediction interval" Confidence interval, definition 363—364 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 364—369 481—482 Confidence interval, for p in binomial distribution 369—371 Confidence interval, for quotient of two variances 585 Confidence interval, for regression coefficients 688 690—691 Confidence interval, for variance of normal distribution 501 Confidence interval, interpretation 365—367 423—424 Confidence interval, relationship to hypothesis testing 585 Consistent estimator 406—409 Consumer’s risk 459 Contingency table 536 628 635 Continuity correction 296—297 contrast 751—756 782—784 Correlation coefficient, applied to linear relationships 707 Correlation coefficient, definition 707 Correlation coefficient, estimate 708—709 Correlation coefficient, in bivariate normal distribution 719—723 Correlation coefficient, interpretation 710 719 Correlation coefficient, relationship to covariance 707 Correlation coefficient, relationship to independence 704 Covariance 702—705 707 Cramer — Rao lower bound 394—397 404—405 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 648—655 663—671 Curve-fitting, method of least squares 647—648 Curve-fitting, residual 650 Curve-fitting, residual plot 650—655 Curve-fitting, transformations to induce linearity 662—663 666 668—669 671 Data transformations 758—760 De Moivre — Laplace limit theorem 292—293 301—302 de Morgan’s laws 35 Density function see "Probability density function (pdf)" Density-scaled histogram 165—168 291 339—340 359—362 Dependent samples 524—525 773—774 792—793 796—800 Distribution-free statistics see "Nonparametric statistics" Efficiency 388—393 396 Efficient estimator 395—396 Estimation see also "Confidence interval" Estimation, Bayesian 410—422 Estimation, least squares 647—648 Estimation, maximum likelihood 344—354 Estimation, method of moments 357—362 Estimation, point versus interval 363—364 Estimator see also "Confidence interval" Estimator, best 396 Estimator, consistent 408—409 Estimator, Cramer — Rao lower bound 394 Estimator, difference between estimate and estimator 346 349 Estimator, efficient 396 Estimator, for binomial p 344—346 380—381 394—395 Estimator, for bivariate normal parameters 721 Estimator, for contrast 752—753 Estimator, for correlation coefficient 708—709 Estimator, for exponential parameter 351 385—386 Estimator, for gamma parameters 359—362 Estimator, for geometric parameter 348—349 Estimator, for normal parameters 353—354 383—384 Estimator, for Poisson parameter 352—353 402 411—412 422 Estimator, for slope and gamma-intercept (linear model) 679—681 Estimator, for uniform parameter 382—383 390—391 403 407 424—426 Estimator, for variance in linear model 683—684 Estimator, interval 363—364 Estimator, sufficient 398 401—402 Estimator, unbiasedness 381—385 Event 24 Expected value, conditional 677—679 Expected value, definition 175 199—201 Expected value, examples 174—182 227—228 Expected value, in method of moments estimation 357—358 Expected value, of functions 186—187 226—227 232—233 320—321 Expected value, of linear combinations 229 Expected value, of loss functions 420 Expected value, of sums 229—232 Expected value, relationship to median 182—183 Expected value, relationship to moment-generating function 261 Experiment 24 Experimental design 523 527—528 538—540 733 773—774 780 792—793 796—800 Exponential distribution, examples 161—163 167—168 183 222—223 242—243 290—292 333—337 351 Exponential distribution, memoryless property 256 Exponential distribution, moment-generating function 259 Exponential distribution, Moments 263 Exponential distribution, parameter estimation 351 385—386 Exponential distribution, relationship to Poisson distribution 289—290 Exponential distribution, threshold parameter 351 Exponential form 405 Exponential regression 662—666 F distribution, definition 475 F distribution, in analysis of variance 738—739 754—755 777 F distribution, in inferences about variance ratios 569 585 F distribution, relationship to chi square distribution 475 F distribution, relationship to Student t distribution 476—477 F distribution, table 476 857—871 Factorization theorem 403 Finite correction factor 375 Fisher’s lemma 516 Friedman’s test 832—833 848—849 Gamma distribution, additive property 330 Gamma distribution, definition 327 329 Gamma distribution, examples 328—329 331 359—362 Gamma distribution, moment-generating function 332 Gamma distribution, Moments 330 Gamma distribution, parameter estimation 359—362 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 464—465 516—521 569 577 593—595 607—608 735 Geometric distribution, definition 317—318 Geometric distribution, examples 317—321 Geometric distribution, memoryless property 319—320 Geometric distribution, moment-generating function 258 318 Geometric distribution, Moments 262 318 Geometric distribution, parameter estimation 348—349 Geometric distribution, relationship to negative binomial distribution 322 Geometric mean 385—386 Geometric probability 207—209 Hazard rate 173 Hypergeometric distribution, definition 139 155 Hypergeometric distribution, examples 141—146 Hypergeometric distribution, Moments 177 375 706 Hypergeometric distribution, relationship to binomial distribution 138—139 Hypothesis testing, critical region 433 Hypothesis testing, decision rule 428—432 455—459 Hypothesis testing, level of significance 434 Hypothesis testing, P-value 437—438 Hypothesis testing, Type I and Type II errors 447—459 747 Independence, effect of, on the expected value of a product 233 Independence, mutual versus pairwise 75—76 Independence, of events 44 70—72 75—77 627—630 Independence, of random variables 216 218 Independence, of regression estimators 683 728—731 Independence, of repeated trials 78—83 Independence, of sample mean and sample variance (normal data) 474 514—516 Independence, of sums of squares 737 Independence, tests for 627—631 Independent samples 524—525 529—532 554 733 796—800 822 826 Intersection 28 Interval estimate see "Prediction interval" Joint cumulative distribution function 213—215 Joint probability density function 203—207 215 k-sample data 531—532 733—734 826—827 Kruskal — Wallis test 826—830 841—848 kurtosis 200—201 Law of small numbers 284—285 level of significance 434 437 447—448 457—458 747 Likelihood function 347 Likelihood ratio see "Generalized likelihood ratio" Linear model, assumptions 677—679 Linear model, confidence intervals for parameters 688 690—691 Linear model, hypothesis tests 685 690—691 697 Linear model, parameter estimation 678—679 683—684 Logarithmic regression 666—668 Logistic regression 668—669 Loss function 419—422 Margin of error 372 423—424 Marginal probability density function 205 211—212 417 Maximum Likelihood Estimation see also "Estimation" Maximum likelihood, estimation definition 347 Maximum likelihood, estimation examples 344—346 348—354 679 Maximum likelihood, estimation in goodness-of-fit testing 615—616 Maximum likelihood, estimation in regression analysis 679 683—684 Maximum likelihood, estimation properties 404—405 409 Mean free path 181 Mean square 740 Median 182—183 388 804 Median unbiased 388 Method of least squares see "Estimation" Method of moments see "Estimation" Minimum variance estimator 395 MINITAB calculations for cdf 272—273 337—338 MINITAB calculations for completely randomized one-factor design 762—764 MINITAB calculations for confidence intervals 366 512—513 596—597 MINITAB calculations for critical values 512 MINITAB calculations for Friedman’s test 848—849 MINITAB calculations for histograms 339—340 MINITAB calculations for independence 644—645 726—727 MINITAB calculations for Kruskal — Wallis test 847—848 MINITAB calculations for Monte Carlo analysis 333—339 366 385—386 424—426 432 MINITAB calculations for one-sample t test 513—514 MINITAB calculations for pdf 272 337 444 MINITAB calculations for randomized block design 800—801 MINITAB calculations for regression analysis 726—728 MINITAB calculations for robustness 495—498 MINITAB calculations for sample statistics 510—511 MINITAB calculations for Tukey confidence intervals 764—766 MINITAB calculations for two-sample t test 595—597 Model equation 529—537 Moment-generating function, as technique for finding distributions of sums 267 Moment-generating function, definition 257 Moment-generating function, examples 258—260 311 Moment-generating function, in proof of central limit theorem 341—342 Moment-generating function, properties 261 266 Moment-generating function, relationship to moments 261 Moments see "Variance" Moore’s Law 663—666 Multinomial coefficients 101 Multinomial distribution 600—603 607 Multiple comparisons 747—750 Multiplication rule 86 Mutually exclusive events 29 71 Negative binomial distribution 157 322—326 Noncentral chi square distribution 767 Noncentral F distribution 768—769 Noninformative prior 412 Nonparametric statistics 803 Normal distribution, additive property 312 Normal distribution, approximation to Binomial distribution 292—293 297—299 338—339 Normal distribution, approximation to Poisson distribution 305—306 Normal distribution, approximation to sign test 804 Normal distribution, approximation to Wilcoxon signed rank statistic 817 Normal distribution, as limit for Student t distribution 470—472 478—479 Normal distribution, central limit theorem 302 341—342 Normal distribution, confidence interval for mean 364—369 482—485 582—585 Normal distribution, confidence interval for variance 501—504 Normal distribution, definition 308 Normal distribution, hypothesis test for mean (variance known) 435 Normal distribution, hypothesis test for mean (variance unknown) 490 493—498 Normal distribution, hypothesis test for variance 504
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