Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner. This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students. Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods
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Putting these pieces together, we have β1 − β2 ≥ 0, so the power for our likelihood ratio test in the Neyman–Pearson lemma is at least as large as the power for any other test with size α. Corollary to the Neyman–Pearson lemma: The ...
Dennis Wackerly, William Mendenhall, Richard L. Scheaffer ... Find the probability that the rth patient is the first emergency case ... The experiment consists of watching patient arrivals until the first emergency case appears.
This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics.
Pearson, K. (1900). On a criterion that a given system of deviations from the probably in the case of a correlated system of variables is such that it can be reasonably be supposed to have arisen from random sampling.
How should the process adopt to the mechanism of the boy (now a young man) who uses his own money to buy a car? Simply continuing to merely count coin and paper money value as a measure of his independently acquired wealth would ...
Integrating the theory and practice of statistics through a series of case studies, each lab introduces a problem, provides some scientific background, suggests investigations for the data, and provides a summary of the theory used in each ...
This book provides students who have already taken three or more semesters of calculus with the background to apply statistical principles.
Example 1.17 How many toys to buy? Assuming that the number of children in the family follows a Poisson distribution with X = 2.4, how many toys should one buy so that every child gets a present.
Noted for its integration of real-world data and case studies, this text offers sound coverage of the theoretical aspects of mathematical statistics.