On Poisson Quasi-Lindley Distribution and its Applications

This paper proposes a recent version of compound Poisson distributions named the Poisson quasi-Lindley (PQL) distribution by compounding Poisson and quasi-Lindley distributions. Some properties of the distributions are given with estimation and some illustrative examples

On the one parameter unit-Lindley distribution and its associated regression model for proportion data

In this paper considering the transformation $X=\frac{Y}{1+Y}$, where $Y \sim\text{Lindley}(\theta)$, we propose the unit-Lindley distribution and investigate some of its mathematical properties. A important fact associated with this new distribution is that is possible to obtain the analytical expression for bias correction of the maximum likelihood estimator. Moreover, it belongs to the exponential family. This distribution allows us to incorporate covariates directly in the mean and consequently to quantify the influence on the average of the response variable. Finally, a practical application is present and it is shown that our model fits much better than the Beta regression.Comment: 17 pages, 4 figure

A bounded distribution derived from the shifted Gompertz law

A two-parameter probability distribution with bounded support is derived from the shifted Gompertz distribution. It is shown that this model corresponds to the distribution of the minimum of a random number with shifted Poisson distribution of independent random variables having a common power function distribution. Some statistical properties are written in closed form, such as the moments and the quantile function. To this end, the incomplete gamma function and the Lambert W function play a central role. The shape of the failure rate function and the mean residual life are studied. Analytical expressions are also provided for the moments of the order statistics and the limit behavior of the extreme order statistics is established. Moreover, the members of the new family of distributions can be ordered in terms of the hazard rate order. The parameter estimation is carried out by the methods of maximum likelihood, least squares, weighted least squares and quantile least squares. The performance of these methods is assessed by means of a Monte Carlo simulation study. Two real data sets are used to illustrate the usefulness of the proposed distribution

Score-based likelihood ratios and sparse Gaussian processes

This thesis concerns two main topics: score-based likelihood ratios (SLRs) for the evaluation of the strength of forensic evidence, and knot selection in sparse Gaussian processes. The work on the first topic seeks to theoretically and empirically justify the use of SLRs in court in place of full, feature-based likelihood ratios (LRs) which are rarely possible to calculate. We show that while the discrepancy between an SLR and the true LR can be unbounded, general probabilistic bounds on an LR given a score exist. These bounds show that the SLR will usually behave reasonably, and will tend to yield the same categorical decisions as the use of the full LR. We also study the problem of selecting a score in the case that the population of sources that possibly generated the relevant evidence of unknown origin is finite. We propose a bivariate performance measure of a score that directly ties to the sufficiency of the score for the forensic hypothesis in question. We then show that the most common scores, measures of dissimilarity between two pieces of evidence, can typically be improved via a general strategy for modifying the score function. We also propose a method to aggregate scores, partially addressing the problem of selecting a score function, via sparse GPs. Thus, we find an application of the second topic in this dissertation to the first topic. Finally, two chapters are dedicated to the study of a proposed method of efficient knot selection in sparse Gaussian processes. Our algorithm is applicable to many types of data and several different objective functions or inferential algorithms. We demonstrate that our algorithm can appropriately select the number and locations of knots so that the resulting predictions are competitive with both a full Gaussian process and models resulting from the currently standard knot selection methods. However, our algorithm tends to train models several times faster. Our algorithm is successfully applied in the chapter on score selection and aggregation for SLRs

Simulation of the mechanical and flow behaviour of bone fixation implants

Titanium (Ti) porous foams produced by additive manufacturing (AM) techniques are promising for fixation devices in orthopaedic applications. These implants should possess sufficient permeability to allow vascular invasion, integration with the host tissue and also satisfy the transport requirements of remodelling bone. The mechanical properties of implants should also match those of the host tissue to ensure sufficient life span in the body. Both macro and micro-structures of implants influence the mechanical and flow properties. Techniques are therefore needed to characterise the structural parameters and to evaluate their effects on the performance of the implant. This thesis focuses on computational modelling tools based on X-ray microtomography (μCT) images to characterise the flow and mechanical properties of porous foams. The aim of the study is to develop and apply these tools on Ti implants with different structures to investigate how the design variables offered by AM technique can be used to alter the implant architecture on multiple length scales to control and tailor the flow and mechanical properties. A computational fluid dynamics model was developed to predict permeability of the implant and how AM can be used to tailor implant flow properties by controlling surface roughness at a microstructual level (microns), and by altering the strut connectivity and density at a macroscopic level (millimetre). A finite element (FE) model of compression test was developed to quantify mechanical properties of the porous implant based on three-dimensional (3D) μCT images and the work is validated and compared to the in situ experiment using μCT. Fluid flow in bone tissue has a key role in the bone remodelling process. A 3D microscale numerical model that simulates the fluid flow-induced shear stress and time dependant bone growth was developed and showed the inter-relationship between those two dynamic factors.Open Acces

Search for resonant pair production of Higgs bosons in the b\bar{b}b\bar{b} pp collisions at \sqrt{s} = 13 TeV

A search for resonant Higgs boson pair production in the b\bar{b}b\bar{b} The analysis uses fb^{-1} -139 fb^{-1} of pp collision data at \sqrt{s} = 13 TeV collected with the ATLAS detector at the Large Hadron Collider. The analysis is divided into two channels, targeting Higgs boson decays which are reconstructed as pairs of small-radius jets or as individual large-radius jets. Spin-0 and spin-2 benchmark signal models are considered, both of which correspond to resonant HH production via gluon-gluon fusion. The data are consistent with Standard Model predictions. Upper limits are set on the production cross section times branching ratio to Higgs boson pairs of a new resonance in the mass range from 251 GeV to 5 TeV

Proceedings of the 2009 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory

The joint workshop of the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, and the Vision and Fusion Laboratory (Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)), is organized annually since 2005 with the aim to report on the latest research and development findings of the doctoral students of both institutions. This book provides a collection of 16 technical reports on the research results presented on the 2009 workshop