Bivariate Discrete Distributions by Kocherlakota – A Comprehensive Statistical Reference for Researchers and Students

Introduction

Bivariate discrete distributions form the backbone of advanced statistical modeling, especially in fields where data naturally occur in paired counts or categories. Written by the distinguished scholar Kocherlakota, this hardbound reference from CRC Press is an essential addition to the library of every serious statistician, data scientist, and academic researcher in India. The book offers a rigorous yet accessible treatment of bivariate discrete distributions, bridging the gap between theoretical foundations and practical applications.

Book Overview

This comprehensive volume systematically explores the major bivariate discrete distributions that have been developed and applied in statistical literature. From the bivariate Poisson and binomial to more specialized families like the bivariate negative binomial and Waring distributions, the author provides an in-depth examination of their structural properties, generating functions, and moment relationships. The text is designed to be self-contained, assuming only a first course in mathematical statistics, making it suitable for postgraduate students and early-career researchers in Indian universities.

Key Highlights

• Comprehensive Coverage: Detailed treatment of bivariate Poisson, binomial, negative binomial, logarithmic series, and other discrete families.
• Sampling Schemes: Development of distributions through realistic sampling mechanisms relevant to Indian survey data.
• Compounding Techniques: Exploration of how compounding leads to richer distribution families.
• Accident Theory Applications: Coverage of Waring and short distributions, crucial for actuarial science and insurance studies in India.
• Inference Methods: Practical statistical inference techniques tailored for discrete bivariate data.

Inside the Book

The book is structured to guide the reader from basic concepts to advanced topics. It begins with a general introduction to discrete distributions, including generating functions and moment relationships. Subsequent chapters delve into specific distributions, each treated with clarity and depth. The author emphasizes interrelationships among distributions, showing how one family can be derived from another. Over 1000 equations support the theoretical exposition, while computer simulation techniques for these distributions are also discussed—a valuable resource for modern data analysis.

Key Topics

• Structural properties of bivariate discrete distributions
• Probability generating functions and moment generating functions
• Bivariate Poisson and its extensions
• Bivariate binomial and negative binomial families
• Compound and mixture distributions
• Waring distribution and its applications in accident theory
• Estimation and hypothesis testing for discrete bivariate data
• Simulation methods for bivariate discrete random variables

Reader Benefits

• Deep Understanding: Gain a thorough grasp of the mathematical underpinnings of bivariate discrete models.
• Practical Skills: Learn how to apply these distributions to real-world data from Indian agriculture, epidemiology, insurance, and social sciences.
• Research Foundation: Build a solid base for pursuing advanced research in multivariate statistics.
• Self-Study Friendly: Clear explanations and worked examples make it ideal for independent learning.
• Reference Value: A go-to resource for statisticians needing to model count data with dependence.

Learning Outcomes

By the end of this book, readers will be able to identify appropriate bivariate discrete distributions for given data sets, derive key properties using generating functions, perform parameter estimation using maximum likelihood and method of moments, conduct hypothesis tests for independence and goodness-of-fit, and simulate bivariate discrete data for further analysis. These skills are directly applicable to Indian statistical practice, from analyzing household survey data to modeling disease counts in epidemiology.

Who Should Read

• Postgraduate Students: In statistics, mathematics, and data science programs across Indian universities.
• Academic Researchers: Working in biometrics, econometrics, actuarial science, and public health.
• Professional Statisticians: In government agencies, research institutes, and private sector analytics teams.
• Faculty Members: Teaching courses on discrete distributions or multivariate analysis.
• Data Scientists: Dealing with count data and seeking robust modeling techniques.

About the Author

Kocherlakota is a highly respected figure in the field of statistical distributions, with decades of teaching and research experience. Known for his clear and methodical writing style, he has contributed significantly to the literature on multivariate discrete distributions. His expertise ensures that this book is both authoritative and accessible, making complex concepts understandable for Indian students and professionals alike.

About the Publisher

CRC Press is a globally recognized publisher of scientific and technical books, known for its high-quality content in mathematics, statistics, and engineering. With a commitment to academic excellence, CRC Press has been a trusted partner for scholars worldwide. This edition, available in India through Bookshops.in, upholds the publisher's tradition of delivering rigorous and well-edited reference works.

Conclusion

Bivariate Discrete Distributions by Kocherlakota is an indispensable resource for anyone serious about mastering discrete bivariate models. Its blend of theoretical depth, practical insight, and comprehensive coverage makes it a standout choice for Indian readers. Whether you are a student preparing for competitive exams like the UGC-NET or GATE in statistics, a researcher analyzing complex survey data, or a professional seeking to enhance your analytical toolkit, this book will serve as a reliable companion. Order your hardcover copy from Bookshops.in today and elevate your understanding of bivariate discrete distributions.