Advances in Statistics - Theory and Applications

1. Front Matter

   Pages i-xxxviii

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2. Ordered Data Analysis

   1. Front Matter

      Pages 1-1

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   2. A Record-Based Transmuted Family of Distributions

      • N. Balakrishnan, M. He

      Pages 3-24

   3. Large-Sample Properties of Jackknife Estimators of the Variance of a Sample Quantile

      • Haikady N. Nagaraja, Chaitra H. Nagaraja

      Pages 25-42

   4. Properties of System Lifetime in the Classical Model with I.I.D. Exponential Component Lifetimes

      • Tomasz Rychlik, Magdalena Szymkowiak

      Pages 43-66

3. Univariate Distribution Theory

   1. Front Matter

      Pages 67-67

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   2. A Note on the Product of Independent Beta Random Variables

      • Filipe J. Marques, Indranil Ghosh, Johan Ferreira, Andriëtte Bekker

      Pages 69-83

   3. On the Distribution of the Product of Independent Beta Random Variables — Applications

      • Carlos A. Coelho, Rui P. Alberto

      Pages 85-117

   4. On the Exact Statistical Distribution of Econometric Estimators and Test Statistics

      • Yong Bao, Xiaotian Liu, Aman Ullah

      Pages 119-131

   5. Hidden Truncation in Non-Normal Models: A Brief Survey

      • Indranil Ghosh, Hon Keung Tony Ng

      Pages 133-160

4. Multivariate Distribution Theory

   1. Front Matter

      Pages 161-161

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   2. Our Joint Work with Barry Arnold: Conditional Specification and Other Topics

      • Enrique Castillo, José María Sarabia

      Pages 163-180

   3. On the Asymptotic Joint Distribution of Multivariate Sample Moments

      • Reinaldo B. Arellano-Valle, Simone B. Harnik, Marc G. Genton

      Pages 181-206

   4. Tail Behavior for Bivariate Distributions Based on Pareto Mixtures

      • Vincenzo Coia, Harry Joe, Natalia Nolde

      Pages 207-228

5. General

   1. Front Matter

      Pages 229-229

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   2. How and Why Did Probability Theory Come About?

      • Nozer D. Singpurwalla, Boya Lai

      Pages 231-242

6. Goodness-of-Fit Tests

   1. Front Matter

      Pages 243-243

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   2. Assessment of Distributional Goodness-of-Fit for Modeling the Superposition of Renewal Process Data

      • Wei Zhang, William Q. Meeker

      Pages 245-270

   3. Goodness-of-Fit Tests for Cauchy Distributions Using Data Transformations

      • J. A. Villaseñor, E. González-Estrada

      Pages 271-282

7. Statistical Inference

   1. Front Matter

      Pages 283-283

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This edited collection brings together internationally recognized experts in a range of areas of statistical science to honor the contributions of the distinguished statistician, Barry C. Arnold. A pioneering scholar and professor of statistics at the University of California, Riverside, Dr. Arnold has made exceptional advancements in different areas of probability, statistics, and biostatistics, especially in the areas of distribution theory, order statistics, and statistical inference. As a tribute to his work, this book presents novel developments in the field, as well as practical applications and potential future directions in research and industry. It will be of interest to graduate students and researchers in probability, statistics, and biostatistics, as well as practitioners and technicians in the social sciences, economics, engineering, and medical sciences.

• distribution theory
• multivariate distributions
• statistical inference
• order statistics
• majorization in Lorenz curve
• characterization
• Bayes

• Department of Mathematics and Statistics, University of North Carolina Wilmington, Wilmington, USA

  Indranil Ghosh

• Department of Mathematics and Statistics, McMaster University, Hamilton, Canada

  N. Balakrishnan

• Department of Statistical Science, Southern Methodist University, Dallas, USA

  Hon Keung Tony Ng

Indranil Ghosh is an Associate Professor of Statistics in the Department of Mathematics and Statistics at the University of North Carolina Wilmington, USA. Currently, he is serving as a guest editor for a special issue of the journal Computational and Mathematical Methods (John Wiley & Sons) and on the editorial board of the Journal of Business Analytics (Taylor & Francis), and is an associate editor for the Journal of the Iranian Statistical Society. He is the Chair-Elect 2021 of the Section on Risk Analysis of the American Statistical Association, and an elected member of the International Statistical Institute.


Narayanaswamy Balakrishnan, Distinguished University Professor, is in the Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada. Professor Balakrishnan is an internationally recognized expert on many areas of statistics, including statistical distribution theory and ordered data analysis. He is currently the Editor-in-Chief of Communications in Statistics (Taylor & Francis), and was previously the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences (John Wiley & Sons). He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics, and in 2016 he received an Honorary Doctorate from The National and Kapodistrian University of Athens, Greece.


Hon Keung Tony Ng is a Professor of Statistical Science with the Southern Methodist University, Dallas, TX, USA. He is an associate editor of Communications in Statistics, Computational Statistics, IEEE Transactions on Reliability, Journal of Statistical Computation and Simulation, Naval Research Logistics, Sequential Analysis and Statistics & Probability Letters. His research interests include reliability, censoring methodology, ordered data analysis, nonparametric methods, and statistical inference. He is the co-editor of Ordered Data Analysis, Modeling and Health Research Methods, Statistical Modeling for Degradation Data, and Statistical Quality Technologies: Theory and Practice (all published by Springer). He is a Fellow of the American Statistical Association, an elected senior member of IEEE and an elected member of the International Statistical Institute.

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