7,946 research outputs found
Efficient sequential designs with asymptotic second-order lower bound of Bayes risk for estimating product of means
Title from PDF of title page viewed January 8, 2020Dissertation advisor: Kamel Rekab and Deep Medhi,VitaIncludes bibliographical references (page 60-62)Thesis (Ph.D.)--Department of Mathematics and Statistics, School of Computing and Engineering. University of Missouri--Kansas City, 2019In order to estimate the reliability of sequentially designed procedures under the Bayesian framework with conjugate priors, a sharp lower bound for the Bayes risk has been derived. Chapter 1 and 2 introduce the background and fundamental concepts and theorems of this study. Chapter 3 focuses on deriving second-order efficiency of Bayes risk for two independent components in the one-parameter exponential family which includes the most common distribution in application of reliability testing, Bernoulli distribution. Chapter 3 also uses Monte Carlo simulations with several proposed sequential designs to illustrate optimality of the second-order efficiency. Then Chapter 4 extends the result to k (k>2) independent components sequentially designed systems. The same Monte Carlo simulations were performed to assure that the second order lower bound is achieved.Introduction -- Conceptual framework -- Second-order efficiency for estimating product of 2 components in exponential family -- Second-order efficiency for estimating product of K components -- Conclusio
Network analysis of the worldwide footballer transfer market
The transfer of football players is an important part in football games. Most
studies on the transfer of football players focus on the transfer system and
transfer fees but not on the transfer behavior itself. Based on the 470,792
transfer records from 1990 to 2016 among 23,605 football clubs in 206 countries
and regions, we construct a directed footballer transfer network (FTN), where
the nodes are the football clubs and the links correspond to the footballer
transfers. A systemic analysis is conduced on the topological properties of the
FTN. We find that the in-degrees, out-degrees, in-strengths and out-strengths
of nodes follow bimodal distributions (a power law with exponential decay),
while the distribution of link weights has a power-law tail. We further figure
out the correlations between node degrees, node strengths and link weights. We
also investigate the general characteristics of different measures of network
centrality. Our network analysis of the global footballer transfer market sheds
new lights into the investigation of the characteristics of transfer
activities.Comment: 7 pages, 6 figure
Weiqi games as a tree: Zipf's law of openings and beyond
Weiqi is one of the most complex board games played by two persons. The
placement strategies adopted by Weiqi players are often used to analog the
philosophy of human wars. Contrary to the western chess, Weiqi games are less
studied by academics partially because Weiqi is popular only in East Asia,
especially in China, Japan and Korea. Here, we propose to construct a directed
tree using a database of extensive Weiqi games and perform a quantitative
analysis of the Weiqi tree. We find that the popularity distribution of Weiqi
openings with a same number of moves is distributed according to a power law
and the tail exponent increases with the number of moves. Intriguingly, the
superposition of the popularity distributions of Weiqi openings with the number
of moves no more than a given number also has a power-law tail in which the
tail exponent increases with the number of moves, and the superposed
distribution approaches to the Zipf law. These findings are the same as for
chess and support the conjecture that the popularity distribution of board game
openings follows the Zipf law with a universal exponent. We also find that the
distribution of out-degrees has a power-law form, the distribution of branching
ratios has a very complicated pattern, and the distribution of uniqueness
scores defined by the path lengths from the root vertex to the leaf vertices
exhibits a unimodal shape. Our work provides a promising direction for the
study of the decision making process of Weiqi playing from the angle of
directed branching tree.Comment: 6 Latex pages including 6 figure
Tur\'an number of the odd-ballooning of complete bipartite graphs
Given a graph , the Tur\'an number is the maximum
possible number of edges in an -vertex -free graph. The study of Tur\'an
number of graphs is a central topic in extremal graph theory. Although the
celebrated Erd\H{o}s-Stone-Simonovits theorem gives the asymptotic value of
for nonbipartite , it is challenging in general to
determine the exact value of for . The
odd-ballooning of is a graph such that each edge of is replaced by an
odd cycle and all new vertices of odd cycles are distinct. Here the length of
odd cycles is not necessarily equal. The exact value of Tur\'an number of the
odd-ballooning of is previously known for being a cycle, a path, a tree
with assumptions, and . In this paper, we manage to obtain the exact
value of Tur\'an number of the odd-ballooning of with , where and each odd cycle has length at
least five.Comment: 16 page
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