Advances in Distribution Theory, Order Statistics, and Inference / Edition 1

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Barry Arnold has made fundamental contributions to many different areas of statistics, including distribution theory, Bayesian inference, multivariate analysis, bounds and orderings, and characterization problems. Organized to honor Arnold's significant contributions to the field, this volume is an outgrowth of the "International Conference on Distribution Theory, Order Statistics, and Inference," held at the University of Cantabria, Santander, Spain. Several distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized. The volume is classified into the following five parts, according to the focus of the articles: Discrete distributions and applications Continuous distributions and applications Order statistics and applications Reliability and applications Inference This comprehensive reference work will serve the statistical and applied mathematics communities, as well as practitioners, researchers, and graduate students in applied probability and statistics, reliability engineering, and biostatistics.

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Editorial Reviews

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From the reviews:
“This volume, which is written in the honour of Professor Barry C. Arnold, reflects his diverse interests and recognizes his important contributions to different areas of statistics (e.g., order statistics, distribution theory, Bayesian inference … and characterization problems). … This book marks the main advances in these areas of research containing theory, methods, applications and extensive bibliographies. All these elements recommend this work as a significant scientific contribution and an important instrument for researchers and graduate students in the areas of statistics and applied mathematics.” (Lucian Maticiuc, Iasi Polytechnic Magazine, Vol. 21 (1/4), March/December, 2009)
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Product Details

  • ISBN-13: 9780817643614
  • Publisher: Birkhauser Verlag
  • Publication date: 5/17/2006
  • Series: Statistics for Industry and Technology Series
  • Edition description: 2006
  • Edition number: 1
  • Pages: 484
  • Product dimensions: 10.00 (w) x 7.00 (h) x 1.19 (d)

Table of Contents


Barry C. Arnold: Career and Accomplishments



List of Tables

List of Figures

Part I: Discrete Distributions and Applications

P.J. Boland and H. Singh: Shastic Comparisons of Bernoulli Sums and Binomial Random Variables

C. Lefèvre: Stopped Compound Poisson Process and Related Distributions

C.D. Lai: Constructions of Discrete Bvariate Dstributions

Part II: Continuous Distributions and Applications

W.J. Reed: The Normal–Laplace Distribution and Its Relatives

A. Pewsey: Some Observations on a Simple Means of Generating Skew Distributions

J.M. Sarabia and E. Castillo: Bivariate Distributions Based on the Generalized Three-Parameter Beta Distribution

D.N. Naik and K. Plungpongpun: A Kotz-Type Distribution for Multivariate Statistical Inference

H. Joe: Range of Correlation Matrices for Dependent Random Variables with Given Marginal Distributions

M.D. Ruiz-Medina and J.M. Angulo: Multifractional Probabilistic Laws

Part III: Order Statistics and Applications

H.A. David: Topics in the History of Order Statistics

H.N. Nagaraja: Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics

N. Balakrishnan and T. Li: Fisher Information and Tukey's Linear Sensitivity Measure Based on Ordered Ranked Set Samples

M. Asadi, N. Ebrahimi, and G.G. Hamedani, and E.S. Soofi: Information Measures for Pareto Distributions and Order Statistics

O. Guilbaud: Confidence Coefficients of Interpolated Nonparametric Sign Intervals for Medians Under No or Weak Shape Assumptions

R. Gatto and S.R. Jammalamadaka: Small Sample Asymptotics for Higher-Order Spacings

T. Rychlik: Best Bounds on Expectations of L-Statistics from Bounded Samples

Part IV: Reliability and Applications

H.W. Block: The Failure Rates of Mixtures

H. Block, M.R. Dugas, and F.J. Samaniego: Characterizations of the Relative Behavior of Two Systems via Properties of Their Signature Vectors

J. Navarro, J.M. Ruiz, and C.J. Sandoval: Systems with Exchangeable Components and Gumbel Exponential Distribution

Z. Chen, J. Mi, and Y.Y. Zhou: Estimating the Mean of Exponential Distribution from Step-Stress Life Test Data

A. SenGupta: Random Stress-Dependent Strength Models Through Exponential Conditionals Distributions

Part V: Inference

E. Castillo, C. Castillo, A.S. Haid, and J.M. Sarabia: Some New Methods for Local Sensitivity Analysis in Statistics

A. García-Pérez: t-Tests with Models Close to the Normal Distribution

M. Divinsky: Computational Aspect of the Chi-Square Goodness-of-Fit Test Applications

F.J. Girón, E. Moreno, and M.L. Martínez: An Objective Bayesian Procedure for Variable Selection in Regression

T.K. Nayak and A. El-Baz: On Bayesian and Decision-Theoretic Approaches to Statistical Prediction

L. Pardo and M.L. Menéndez: Phi-Divergence-Type Test for Positive Dependence Alternatives in 2 x k Contingency Tables

D. Pena and P. Poncela: Dimension Reduction in Multivariate Time Series

W. Guo, S. Kasala, M.B. Rao, and B. Tucker: The Hat Problem and Some Variations


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