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Statistical distributions are fundamental to Statistical Science and are a prime indispensable tool for its applications. This monograph is the first to examine an important but somewhat neglected field — univariate continuous distribution on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of “novel” contributions developed in recent years, such as the two-sided power, generalized trapezoidal and generalized Topp and Leone distributions, among others. It discusses a general framework for constructing two-sided distributions and some of its properties. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions not emphasized in existing literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures. The applications are drawn mainly from the econometric and engineering domains.
Statistical distributions are fundamental to Statistical Science and are a prime indispensable tool for its applications. This monograph is the first to examine an important but somewhat neglected field — univariate continuous distribution on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of “novel” contributions developed in recent years, such as the two-sided power, generalized trapezoidal and generalized Topp and Leone distributions, among others. It discusses a general framework for constructing two-sided distributions and some of its properties. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions not emphasized in existing literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures. The applications are drawn mainly from the econometric and engineering domains.
The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.
This is a book about statistical distributions, their properties, and their application to modelling the dependence of the location, scale, and shape of the distribution of a response variable on explanatory variables. It will be especially useful to applied statisticians and data scientists in a wide range of application areas, and also to those interested in the theoretical properties of distributions. This book follows the earlier book ‘Flexible Regression and Smoothing: Using GAMLSS in R’, [Stasinopoulos et al., 2017], which focused on the GAMLSS model and software. GAMLSS (the Generalized Additive Model for Location, Scale, and Shape, [Rigby and Stasinopoulos, 2005]), is a regression framework in which the response variable can have any parametric distribution and all the distribution parameters can be modelled as linear or smooth functions of explanatory variables. The current book focuses on distributions and their application. Key features: Describes over 100 distributions, (implemented in the GAMLSS packages in R), including continuous, discrete and mixed distributions. Comprehensive summary tables of the properties of the distributions. Discusses properties of distributions, including skewness, kurtosis, robustness and an important classification of tail heaviness. Includes mixed distributions which are continuous distributions with additional specific values with point probabilities. Includes many real data examples, with R code integrated in the text for ease of understanding and replication. Supplemented by the gamlss website. This book will be useful for applied statisticians and data scientists in selecting a distribution for a univariate response variable and modelling its dependence on explanatory variables, and to those interested in the properties of distributions.
"Papers presented at the symposium in remembrance of prof. Jan M. van Noortwijk on November 24, 2009 in Delft, the Netherlands"--Cover.
Safety and Reliability of Complex Engineered Systems contains the Proceedings of the 25th European Safety and Reliability Conference, ESREL 2015, held 7-10 September 2015 in Zurich, Switzerland. Including 570 papers on theories and methods in the area of risk, safety and reliability, and their applications to a wide range of industrial, civil and social sectors, this book will be of interest to academics and professionals involved or interested in aspect of risk, safety and reliability in various engineering areas.
Agent-based modelling enables the explicit representation of entities and their interaction with each other and the environment, and so it became an important method to study complex systems. Social networks form an important part of agent-based social simulation, as they define the topology of agent interaction. This dissertation initially identifies important properties of social networks and their dynamics and reviews their representation in agent-based models of relevant domains. A classification of levels of detail for the network modelling components initialisation, dynamics of networks, and dynamics on networks is proposed and guides the identification of deficits. A formal, iterative evaluation framework is developed to quantitatively assess network modelling approaches under a set of weighted criteria (representativity, adjustability, validity, and efficiency). The framework is applied to an abstract model of opinion dynamics and to an empirically grounded model of social influence. A lifestyle-specific network survey is designed, conducted, and analysed and helps to ground the evaluation of the network modelling’s representativity on empirical data. The study finds significant differences of degree and distance distributions as well as in the composition of ego networks between lifestyles. New network modelling approaches are developed to account for requirements in agent-based models such as agent-type specific link preferences, degree and distance distributions, community structures, and interaction dynamics. The comparison of simple to elaborated network modelling for the application models shows a significant impact on simulation results, highlighting the need for informed decisions about suitable approaches.
Advances in Clinical Chemistry, Volume 116, the latest release in this internationally acclaimed series, contains chapters authored by world-renowned clinical laboratory scientists, physicians and research scientists. - Provides the most up-to-date technologies in clinical chemistry and clinical laboratory science - Authored by world renowned clinical laboratory scientists, physicians and research scientists - Presents the international benchmark for novel analytical approaches in the clinical laboratory