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.
Preface.- Barry C. Arnold: career and accomplishments.- Publications.- Contributors.- List of tables.- List of figures.- Part I: Discrete distribution and applications.- Stochastic comparisons of Bernoulli sums and binomial random variables.- Stopped compound Poisson process and related distributions.- Constructions of discrete bivariate distributions.- Part II: Continuous distributions and applications.- The normal?Laplace distribution and its relatives.- Some observations on a simple means of generating skew distributions.- Bivariate distributions based on the generalized three-parameter beta distribution.- A Kotz-type distribution for multivariate statistical inference.- Range of correlation matrices for dependent random variables with given marginal distributions.- Multifractional probabilistic laws.- Part III: Order statistics and applications.- Topics in the history of order statistics.- Order statistics from independent exponential random variables and the sum of the top order statistics.- Fisher information and Tukey's linear sensitivity measure based on ordered ranked set samples.- Information measures for Pareto distributions and order statistics.- Confidence coefficients of interpolated nonparametric sign intervals for medians under no or weak shape assumptions.- Small sample asymptotics for higher-order spacings.- Best bounds on expectations of L-statistics from bounded samples.- Part IV: Reliability and applications.- The failure rates of mixtures.- Characterizations of the relative behavior of two systems via properties of their signature vectors.- Systems with exchangeable components and Gumbel exponential distribution.- Estimating the mean of exponential distribution from step-stress life test data.- Random stress-dependent strength models through exponential conditionals distributions.- Part V: Inference.- Some new methods for local sensitivity analysis in statistics.- t-tests with models close to the normal distribution.- Computational aspect of the chi-square goodness-of-fit test applications.- An objective Bayesian procedure for variable selection in regression.- On Bayesian and decision-theoretic approaches to statistical prediction.- Phi-divergence-type test for positive dependence alternatives in 2 x k contingency tables.- Dimension reduction in multivariate time series.- The hat problem and some variations.- Index.