Some Multiple Decision And Related Problems With Special Reference To Restricted Families Of Distributions And Applications To Reliability Theory
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| Author | : Shanti S. Gupta |
| Publisher | : |
| Total Pages | : 96 |
| Release | : 1973 |
| Genre | : |
| ISBN | : |
The paper deals with procedures for selecting a subset from k given populations so as to include the best with a specified guaranteed minimum probability. Some general results relating to subset selection and specific procedures for important classes of distributions are reviewed with special emphasis on restricted families of probability distributions. Such families are defined through partial order relations and are extensively considered in reliability theory. A selection problem for tail-ordered family of distributions is considered and tables are provided for constants needed to implement the procedure. A general partial order relation is defined through a class of real valued functions and a related selection problem is discussed. These results provide a unified view of earlier known results. The rest of the paper gives a brief survey of some important results pertaining to restricted families of distributions such as the star-ordered and convex-ordered distributions. These results relate to life test sampling plans, inequalities for linear combinations of order statistics, estimation of failure rate function and some tests of hypotheses. (Author).
| Author | : Jeffrey Hollis Hooper |
| Publisher | : |
| Total Pages | : 438 |
| Release | : 1977 |
| Genre | : Distribution (Probability theory) |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 438 |
| Release | : 1977 |
| Genre | : Operations research |
| ISBN | : |
| Author | : Ming-Wei Lu |
| Publisher | : |
| Total Pages | : 123 |
| Release | : 1976 |
| Genre | : |
| ISBN | : |
This thesis deals with some selection and ranking procedures for restricted families of probability distributions. A selection rule is proposed for distributions which are convex-ordered with respect to a specified distribution G. Some properties of this selection rule are derived. The asymptotic relative efficiencies of this rule with respect to other selection rules are evaluated. A selection rule is also proposed and studied for distributions which are s-ordered with respect to G. Some interval estimation problems for the unknown parameters of the k populations are studied. The infimum of the probability that a given confidence interval (based on suitably chosen order statistics) contains at least one good population is obtained. Different modifications and variations of this problem are also studied. The selection procedures are discussed in terms of majorization and weak majorization. The parameter is partially ordered by means of majorization or weak majorization. A class of procedures R sub h for selecting the best population is defined.
| Author | : |
| Publisher | : |
| Total Pages | : 1206 |
| Release | : 1974-11 |
| Genre | : |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 258 |
| Release | : 1976-12-24 |
| Genre | : Science |
| ISBN | : |
| Author | : N. Balakrishnan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 439 |
| Release | : 2007-12-28 |
| Genre | : Mathematics |
| ISBN | : 0817644229 |
S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these areas and form a tribute to Panchapakesan’s influence and impact on these areas. Featuring theory, methods, applications, and extensive bibliographies with special emphasis on recent literature, this comprehensive reference work will serve researchers, practitioners, and graduate students in the statistical and applied mathematics communities.
| Author | : Y. L. Tong |
| Publisher | : Academic Press |
| Total Pages | : 256 |
| Release | : 2014-07-10 |
| Genre | : Mathematics |
| ISBN | : 1483269213 |
Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general. Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing. This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.
| Author | : |
| Publisher | : |
| Total Pages | : 982 |
| Release | : 1973 |
| Genre | : Research |
| ISBN | : |
| Author | : S. S. Gupta |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 113 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461259258 |
The theory and practice of decision making involves infinite or finite number of actions. The decision rules with a finite number of elements in the action space are the so-called multiple decision procedures. Several approaches to problems of multi ple decisions have been developed; in particular, the last decade has witnessed a phenomenal growth of this field. An important aspect of the recent contributions is the attempt by several authors to formalize these problems more in the framework of general decision theory. In this work, we have applied general decision theory to develop some modified principles which are reasonable for problems in this field. Our comments and contributions have been written in a positive spirt and, hopefully, these will an impact on the future direction of research in this field. Using the various viewpoints and frameworks, we have emphasized recent developments in the theory of selection and ranking ~Ihich, in our opinion, provides one of the main tools in this field. The growth of the theory of selection and ranking has kept apace with great vigor as is evidenced by the publication of two recent books, one by Gibbons, Olkin and Sobel (1977), and the other by Gupta and Panchapakesan (1979). An earlier monograph by Bechhofer, Kiefer and Sobel (1968) had also provided some very interest ing work in this field.
