Central limit theorems and statistical inference for some random graph models

Random graphs and networks are of great importance in any fields including mathematics, computer science, statistics, biology and sociology. This research aims to develop statistical theory and methods of statistical inference for random graphs in novel directions. A major strand of the research is the development of conditional goodness-of-fit tests for random graph models and for random block graph models. On the theoretical side, this entails proving a new conditional central limit theorem for a certain graph statistics, which are closely related to the number of two-stars and the number of triangles, and where the conditioning is on the number of edges in the graph. A second strand of the research is to develop composite likelihood methods for estimation of the parameters in exponential random graph models. Composite likelihood methods based on edge data have previously been widely used. A novel contribution of the thesis is the development of composite likelihood methods based on more complicated data structures. The goals of this PhD thesis also include testing the numerical performance of the novel methods in extensive simulation studies and through applications to real graphical data sets

Central limit theorems and statistical inference for some random graph models

Random graphs and networks are of great importance in any fields including mathematics, computer science, statistics, biology and sociology. This research aims to develop statistical theory and methods of statistical inference for random graphs in novel directions. A major strand of the research is the development of conditional goodness-of-fit tests for random graph models and for random block graph models. On the theoretical side, this entails proving a new conditional central limit theorem for a certain graph statistics, which are closely related to the number of two-stars and the number of triangles, and where the conditioning is on the number of edges in the graph. A second strand of the research is to develop composite likelihood methods for estimation of the parameters in exponential random graph models. Composite likelihood methods based on edge data have previously been widely used. A novel contribution of the thesis is the development of composite likelihood methods based on more complicated data structures. The goals of this PhD thesis also include testing the numerical performance of the novel methods in extensive simulation studies and through applications to real graphical data sets

Evaluating the system reliability of the bridge structure using the unit half-logistic geometric distribution

The concept of reliability has gained widespread use in various fields, including manufacturing. This paper examines a system consisting of five components, including a bridge network component. The components are assumed to be identical and have a varying failure rate over time, with a unit half-logistic geometric distribution. The study focuses on analyzing properties such as the mean time to failure (MTTF), α-fractiles, and reliability equivalence factor (REF). To improve the bridge system, the reduction and duplication methods are implemented. Numerical results are provided to demonstrate the effectiveness of these methods