© 1999

Scan Statistics and Applications

  • Joseph Glaz
  • N. Balakrishnan

Part of the Statistics for Industry and Technology book series (SIT)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Introduction and Preliminaries

    1. Front Matter
      Pages 1-1
    2. Joseph Glaz, N. Balakrishnan
      Pages 3-24
  3. Discrete Scan Statistics

    1. Front Matter
      Pages 25-25
    2. Joachim Krauth
      Pages 67-96
    3. Joseph I. Naus
      Pages 97-109
  4. Continuous Scan Statistics

  5. Applications

    1. Front Matter
      Pages 249-249
    2. Markos V. Koutras, N. Balakrishnan
      Pages 251-267
    3. Ming-Ying Leung, Traci E. Yamashita
      Pages 269-286
  6. Back Matter
    Pages 323-324

About this book


The study of scan statistics and their applications to many different scientific and engineering problems have received considerable attention in the literature recently. In addition to challenging theoretical problems, the area of scan statis­ tics has also found exciting applications in diverse disciplines such as archaeol­ ogy, astronomy, epidemiology, geography, material science, molecular biology, reconnaissance, reliability and quality control, sociology, and telecommunica­ tion. This will be clearly evident when one goes through this volume. In this volume, we have brought together a collection of experts working in this area of research in order to review some of the developments that have taken place over the years and also to present their new works and point out some open problems. With this in mind, we selected authors for this volume with some having theoretical interests and others being primarily concerned with applications of scan statistics. Our sincere hope is that this volume will thus provide a comprehensive survey of all the developments in this area of research and hence will serve as a valuable source as well as reference for theoreticians and applied researchers. Graduate students interested in this area will find this volume to be particularly useful as it points out many open challenging problems that they could pursue. This volume will also be appropriate for teaching a graduate-level special course on this topic.


Approximation DNA sequence approach Markov Monte Carlo simulation calculus continuous scan statistics discrete scan statistics finite Markov chain imbedding model observed cluster of events order statistics probability models spatial scan stat

Editors and affiliations

  • Joseph Glaz
    • 1
  • N. Balakrishnan
    • 2
  1. 1.Department of StatisticsUniversity of Connecticut at StorrsStorrsUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

Bibliographic information


"...The subject can be quite exciting to probabilists, researchers and graduate students learning about these techniques in relation to scan statistics as a central point. The chapters are well written in a review style, discussing the main issues of scan statistics in a particular topic, and presenting the motivation and the main results, mostly without proving them. Proofs can be found in the related original papers. However, some hints and discussions are given on how to derive certain results. A few new results are scattered throughout. The book contains a useful short subject index..." —Mathematical Reviews

"The area of scan statistics is very complex with a variety of exciting theoretical results and plethora of useful applications. There are many techniques which can be used in solving problems in this area. Up to now the results were spread out in different journals. There was a need for a book consolidating the knowledge on scan statistics and providing a comprehensive survey of all the developments in this area of research. The book by Glaz and Balakrishnan achieves this and will serve as a basic reference for theoreticians and applied researchers involved or interested in scan statistics. It presents new results, describes applications of scan statistics, points out many challenging open problems for research and gives valuable references which might be of particular interest to graduate students...

To sum up, the book 'Scan Statistics and Applications,' edited by Glaz and Balakrishnan, contains excellent contributions. I enjoyed every chapter as well as the whole book. It would be interesting to have an update of the book in a few years to appreciate the developments and new results on scan statistics. The present edition of the book is good value for money."  —Extremes

"...The monograph we are reviewing clearly outlines the high interest and the broad applicability of scan statistics as a tool to analyse the occurence of observed clusters of events in time and space. 'Scan Statistics and Applications' is a comprehensive and fine edited survey that brings together results due to leading authorities in this new area of statistical research and its applications. Each chapter is closed by a rich reference list, which allows the interested reader to go deeper in one topic or another. The technical presentation of the volume is of a high level—a well-established feature of the books edited by Birkhauser Verlag in the SIT Series." —Analele Stiintifice ale Universitatii "Al.I. Cuza" Iasi

"Scan statistics have been studied and used for more than fifty years, but the present book tries to make the scattered information on this topic available in a condensed form for the first time.... The volume is a valuable source book for all researchers who are interested in the state of the art with respect to theoretical results and applications of scan statistics." —Statistics and Decisions