This book tries to explain the difficult ideas in axiomatic approach to the theory in a clear and comprehensive manner. It addresses several unusual distributions including the power series distribution. Readers will find many worked-out examples and exercises with hints, which will make the book easily readable and engaging.
The author is a former professor of the Indian Statistical Institute, India.
Topics include discrete and random variables; functions of random variables; and binomial distributions. The selection also discusses the numerical characteristics of probability distributions; limit theorems and estimates of the mean; and the law of large numbers. The text also describes linear correlation, including conditional expectations and their properties, coefficient of correlation, and best linear approximation to the regression function. The book presents tables that show the values of the normal probability integral, Poisson distribution, and values of the normal probability density.
The text is a good source of data for readers and students interested in probability theory.
The comprehensive text includes a multitude of new examples and exercises, and careful revisions throughout. Particular attention is given to the expansion of the last three chapters of the book with the addition of one entirely new chapter (9) on ’Finding and Comparing Estimators.’ The classroom-tested material presented in this second edition forms the basis for a second course introducing mathematical statistics.
* non-parametric estimation of lifetimes of subjects exposed to radiation
* statistical analysis of simultaneous degradation-mortality data with covariates of the aged
* estimation of maintenance efficiency in semiparametric imperfect repair models
* cancer prognosis using survival forests
* short-term health problems related to air pollution: analysis using semiparametric generalized additive models
* parametric models in accelerated life testing and fuzzy data
* semiparametric models in the studies of aging and longevity
This book will be of use as a reference text for general statisticians, theoreticians, graduate students, reliability engineers, health researchers, and biostatisticians working in applied probability and statistics.
In Knock on Wood, with great humour and irreverence, Rosenthal divines the world of luck, fate and chance, putting his considerable scientific acumen to the test in deducing whether luck is real or the mere stuff of superstition.
The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes.
Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.
This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.
Several distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized. The volume is classified into the following five parts, according to the focus of the articles:
* Discrete distributions and applications
* Continuous distributions and applications
* Order statistics and applications
* Reliability and applications
This comprehensive reference work will serve the statistical and applied mathematics communities, as well as practitioners, researchers, and graduate students in applied probability and statistics, reliability engineering, and biostatistics.
Probability theory is a key part of contemporary mathematics. The subject plays a key role in the insurance industry, modelling financial markets, and statistics in general — including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics, social sciences). Every student majoring in mathematics at university ought to take a course on probability or mathematical statistics. Probability is now a standard part of high school mathematics, and teachers ought to be well versed and confident in the subject. Problem solving is important in mathematics. This book combines problem solving and probability.
These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Key to the presentation is the concentration on the probabilistic and statistical aspects of extreme values without major emphasis on such related topics as regular variation, point processes, empirical distribution functions, and Brownian motion.
The work is an excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity.
One main applicable result of the book involves arriving at a general solution to the canonical detection problem for active sonar in a reverberation-limited environment. Nonetheless, the general problems dealt with in the text also provide a useful framework for discussing other current research areas, such as wavelet decompositions, neural networks, and higher order spectral analysis.
The structure of the book, with the exposition presenting as many details as necessary, was chosen to serve both those readers who are chiefly interested in the results and those who want to learn the material from scratch. Hence, the text will be useful for graduate students and researchers alike in the fields of engineering, mathematics and statistics.