Records and branching processes / Mohammad Ahsanullah and George P. Yanev, editors.

Format:

Book

Contributor:

Ahsanullah, Mohammad.

Yanev, George P.

Language:

English

Subjects (All):

Distribution (Probability theory).

Branching processes.

Mathematical statistics.

Physical Description:

1 online resource (187 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2008.

Language Note:

English

Summary:

This book concerns itself with record values and branching processes as rich research areas of applied probability and statistics. Over the last few decades, numerous interesting articles on these topics appeared, dealing with theoretical problems as well as a number of new applications. The authors have co-ordinated publishing works contributed by eminent researchers from all over the world. This book presents a selection of presentations of new developments and survey papers on the subjects of record values and branching processes. It is written at intermediate level which requires knowledge of probability theory and mathematical statistics.

Contents:

Intro

RECORDS AND BRANCHING PROCESSES

CONTENTS

PREFACE

CONTRIBUTORS AND AFFILIATION

Chapter 2CHARACTERIZATIONS OF DISTRIBUTIONS VIABIVARIATE REGRESSION ON DIFFERENCES OFRECORDS

Abstract

1 Introduction

2 Results and Proofs

2.1 Main result

Acknowledgment

References

Chapter 3REGENERATIVE BRANCHING PROCESSES

2 General Definition

3 BGW Processes with State-dependent Immigration

4 Continuous Time Markov Processes

5 Age-Dependent Branching Processes

6 Alternating Regenerative Processes

7 Continuous-State Branching Processes

8 Branching Processes with Migration

9 Time Non-Homogeneous State-Dependent Immigration

10 Concluding Remarks

Chapter 4CONDITIONAL LIMIT THEOREMSFOR CONTINUOUS TIME AND STATE BRANCHINGPROCESS

2 The CB-Process

3 Attaining the Origin

4 The Critical Case

5 Stationary Measures

6 The Subcritical Case

7 The Last Large Jump

LARGE FAMILIES AND EXCEEDANCES INBRANCHING PROCESSES

2 Exceeding a Threshold

2.1 Sequence of processes with common offspring distribution

2.2 Sequence of processes with distinct offspring distributions

2.3 Extended class of level functions for critical processes

2.4 Processes with immigration

3 Number of Highly Productive Ancestors

4 Large Families in Multitype Processes

Acknowledgments

Chapter 6A REVIEW OF OFFSPRING EXTREMES INBRANCHING PROCESSES

2 Maximum Family Size in Simple Branching Processes

2.1 Subcritical Processes

2.2 Critical Processes

2.3 Supercritical Processes

3 Maximum Family Size in Processes with Varying Environments

3.1 Maxima of Arrays of Zero-Modified Geometric Variables.

3.2 Processes with Varying Geometric Environments

4 Maxima in Bisexual Processes

4.1 Max-Domain of Attraction of Bivariate Geometric Arrays

4.2 Bisexual Processes with Varying Geometric Environments

5 Maximum Score

5.1 Maximum Scores in Galton-Watson Processes

5.2 Maximum Scores in Two-Type Processes

Chapter 7STATISTICAL INFERENCE FOR BRANCHINGPROCESSES

2 Classical BGW Branching Processes

3 BGW Processes with an Increasing Random Numberof Ancestors

3.1 Estimating the Offspring Mean when Z0(n) n a.s.

3.4 Lotka-Nagaev Estimators

3.5 Heyde Moment-Type Estimators

3.6 Estimating the Unknown Age of the Process

3.7 Conditional Least Squares Estimators

3.8 Censored Estimators

3.2 Limiting Distributions

3.3 Harris Estimators

4 BGW Processes with Immigration

5 Concluding Remarks and Comments

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record and CIP data provided by publisher.

ISBN:

1-61470-735-9

OCLC:

923663225