Probability and Statistical Models with Applications

Probability and Statistical Models with Applications

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Description

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probability and Statistical Models with Applications is a must read for probabilists and theoretical and applied statisticians.show more

Product details

  • Hardback | 664 pages
  • 163.8 x 243.8 x 41.4mm | 1,144.58g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 2003.
  • 21 black & white tables
  • 1584881240
  • 9781584881247

Review quote

"the book contains some chapters of interest for probabilists and theoretical and applied statisticians. Most of the articles end with a complete list of references of recent developments, which will make it easier for graduate students and researchers in finding articles of interest." -Short Book Reviews, Vol. 21, No. 2, August 2001 "deserves a place in the central reference section of any university mathematics library." - The Mathematical Gazette, March 1997show more

Table of contents

PREFACE LIST OF CONTRIBUTORS LIST OF TABLES LIST OF FIGURES THEOPHILOS N. CACOULLOS - A VIEW OF HIS CAREER PUBLICATIONS OF THEOPHILOS N. CACOULLOS THE TEN COMMANDMENTS FOR A STATISTICIAN PART I APPROXIMATION, BOUNDS AND INEQUALITIES. NON-UNIFORM BOUNDS IN PROBABILITY APPROXIMATIONS USING STEIN'S METHOD Introduction Poisson Approximation Binomial Approximation: Binary Expansion of a Random Integer Normal Approximation Conclusion PROBABILITY INEQUALITIES FOR MULTIVARIATE DISTRIBUTIONS WITH APPLICATIONS TO STATISTICS Introduction and Summary Positive Dependence and Product-Type Inequalities Negative Dependence and Product-Type Inequalities Bonferroni-Type Inequalities Applications APPLICATIONS OF COMPOUND POISSON APPROXIMATION Introduction First Applications Word Counts Discussion and Numerical Examples COMPOUND POISSON APPROXIMATION FOR SUMS OF DEPENDENT RANDOM VARIABLES Introduction Preliminaries and Notations Main Results Examples of Applications UNIFIED VARIANCE BOUNDS AND A STEIN-TYPE IDENTITY Introduction Properties of the Transformation Application to Variance Bounds PROBABILITY INEQUALITIES FOR U-STATISTICS Introduction Preliminaries Probability Inequalities PART II PROBABILITY AND STOCHASTIC PROCESSES THEORY AND APPLICATIONS OF DECOUPLING Complete Decoupling of Marginal Laws and One-Sided Bounds Tangent Sequences and Conditionally Independent Variables Basic Decoupling Inequalities for Tangent Sequences Applications to Martingale Inequalities and Exponential Tail Probability Bounds Decoupling of Multilinear Forms, U-Statistics and U-Processes Total Decoupling of Stopping Times Principle of Conditioning in Weak Convergence Conclusion A NOTE ON THE PROBABILITY OF RAPID EXTINCTION OF ALLELES IN A WRIGHT-FISHER PROCESS Introduction The Lower Bound for Boundary Sets STOCHASTIC INTEGRAL FUNCTIONALS IN AN ASYMPTOTIC SPLIT STATE SPACE Introduction Preliminaries Phase Merging Scheme for Markov Jump Processes Average of Stochastic Integral Functional Diffusion Approximation of Stochastic Integral Function Integral Functional with Perturbed Kernel BUSY PERIODS FOR SOME QUEUES WITH DETERMINISTIC INTERARRIVAL OR SERVICE TIMES Introduction Preliminaries: A Basic Class of Polynomials The Dg/M(Q)/1 Queue The M(Q)/Dg /1 Queue THE EVOLUTION OF POPULATION STRUCTURE OF THE PERTURBED NON-HOMOGENOUS SEMI-MARKOV SYSTEM Introduction The Perturbed Non-Homogeneous Semi-Markov System The Expected Population Structure with Respect to the First Passage Time Probabilities The Expected Population Structure with Respect to the Duration of a Membership in a State The Expected Population Structure with Respect to the State Occupancy of a Membership The Expected Population Structure with Respect to the Counting Transition Probabilities PART III DISTRIBUTIONS, CHARACTERIZATIONS, AND APPLICATIONS CHARACTERIZATIONS OF SOME EXPONENTIAL FAMILIES BASED ON SURVIVAL DISTRIBUTIONS AND MOMENTS Introduction An Auxiliary Lemma Characterizations Based on Survival Distributions Characterizations Based on Moments BIVARIATE DISTRIBUTIONS COMPATIBLE OR NEARLY COMPATIBLE WITH GIVEN CONDITIONAL INFORMATION Introduction Imprecise Specification Precise Specification An Example A CHARACTERIZATION OF A DISTRIBUTION ARISING FROM ABSORPTION SAMPLING Introduction The Characterization Theorem An Application REFINEMENTS OF INEQUALITIES FOR SYMMETRIC FUNCTIONS GENERAL OCCUPANCY DISTRIBUTIONS Introduction A General Random Occupancy Model Special Occupancy Distributions A SKEW t Distribution Introduction Derivation of Skew t Density Properties of Skew t Distribution A First Bivariate Skew t Distribution A Second Bivariate Skew t Distribution ON THE POSTERIOR MOMENTS FOR TRUNCATION PARAMETER DISTRIBUTIONS AND IDENTIFIABILITY BY POSTERIOR MEAN FOR EXPONENTIAL DISTRIBUTION WITH LOCATION PARAMETERS Introduction Posterior Moments Examples Identifiability by Posterior Mean An Illustrative Example DISTRIBUTIONS OF RADON VOLUMES WITHOUT USING INTEGRAL GEOMETRY TECHNIQUES Introduction Evaluation of Arbitrary Moments of the Random Volumes PART IV TIME SERIES, LINEAR, AND NON-LINEAR SERIES COINTEGRATION OF ECONOMIC TIME SERIES Introduction Regression Models Simultaneous Equation Models Canonical Analysis and the Reduced Rank Regression Estimator Autoregressive Processes Nonstationary Models Cointegrated Models Asymptotic Distribution of Estimators and Test Criterion ON SOME POWER PROPERTIES OF GOODNESS-OF-FIT TESTS IN TIME SERIES ANALYSIS Testing Spectral Density Fits Local Power Considerations Comparison LINEAR CONSTRAINTS ON A LINEAR MODEL Introduction Geometric Interpretation of the Role of the Linear Constraints M-METHODS IN GENERALIZED NONLINEAR MODELS Introduction Definitions and Assumptions Asymptotic Results Test of Significance and Computational Algorithm PART V INFERENCE AND APPLICATIONS EXTENTIONS OF A VARIATION OF THE ISOPERIMETRIC PROBLEM Introduction Information Retrieval Problem Information Retrieval without Measurement Error Useful Information in a Variable Allocation of Storage Space The Isoperimetric Problem Extensions ON FINDING A SINGLE POSITIVE UNIT IN GROUP-TESTING Introduction Description of Properties, Numerical Results Some Formulas for Procedure RDH The Greedy Procedure RG Conclusions Changing the Prior with Procedure RDH Robustness of Procedure RDH for q Known TESTING HYPOTHESES ON VARIANCES IN THE PRESENCE OF CORRELATIONS Bivariate Normal Population Modifying the Hypothesis Non-Null Moments Null Case The Conditional Hypothesis ESTIMATING THE SMALLEST SCALE PARAMETER: UNIVERSAL DOMINATION RESULTS Introduction Main Results ON SENSITIVITY OF EXPONENTIAL RATE OF CONVERGENCE FOR THE MAXIMUM LIKELIHOOD ESTIMATOR Introduction Main Results Some Applications Discussion A CLOSER LOOK AT WEIGHTED LIKELIHOOD IN THE CONTEXT OF MIXTURES Introduction Background Simulation Experiments and Results Model Selection Conclusions ON NONPARAMETRIC FUNCTION ESTIMATION WITH INFINITE-ORDER FLAT-TOP KERNELS Introduction: A General Family of Flat-Top Kernels of Infinite Order Multivariate Density Estimation: A Review Further Issues on Density Estimation MULTIPOLISHING LARGE TWO-WAY TABLES Introduction Bilinear Multipolishers Matrix Approximations Displays Examplel Concluding Remarks ON DISTANCES AND MEASURES OF INFORMATION: A CASE OF DIVERSITY Introduction Measuring Information-Measures of Information Properties of Measures of Information Measures of Information and Inference Applications Conclusions REPRESENTATION FORMULAE FOR PROBABILITIES OF CORRECT CLASSIFICATION Introduction Vector Algebraic Preliminaries Distributional Results ESTIMATION OF CYCLING EFFECT ON RELIABILITY Models Semiparametric Estimation PART VI APPLICATIONS TO BIOLOGY AND MEDICINE A NEW TEST FOR TREATMENT VS. CONTROL IN AN ORDERED 2 X 3 CONTINGENCY TABLE Introduction New Test, Implementation and Example Simulation Study Theoretical Properties Appendix AN EXPERIMENTAL STUDY OF THE OCCURRENCE TIMES OF RARE SPECIES Statement of the Problem The Design of the Experiment Stage 2 of the Experiment Findings A DISTRIBUTION FUNCTIONAL ARISING IN EPIDEMIC CONTROL Introduction Properties of the Functional Proof of the Theorem Application to Epidemic Control BIRTH AND DEATH URN FOR TERNARY OUTCOMES: STOCHASTIC PROCESSES APPLIED TO URN MODELS Introduction A Birth and Death Urn with Immigration for Ternary Outcomes Embedding the Urn Scheme in a Continuous-Time Birth and Death Process The Probabiity Generating Function for the Number of Success on Treatment i in the Continuous-Time Birth and Death Process The Probability Generating Function for the Number of Trials on Treatment i in the Continuous-Time Birth and Death Process The Number of Trials on Treatment i in the Continuous -Time Birth and Death Process The Joint Probability Generating Function for the Number of Successes and the Number of Trials in the Continuous-Time Birth and Death Process Adopting a Stopping Rule to Convert Continuous-Time Statistics to the Urn Design Limiting Results for the Proportion of Trials on Treatment i AUTHOR INDEX SUBJECT INDEX NOTE: References at the end of each chapter.show more