Discrete-continuous dual families and limiting distributions of random sums: the Pareto-Normal case

We explore the framework of location-scale mixtures of Gaussian distributions (SMGD) and consider a special case where the conditional mean and variance follow the Pareto Type II (Lomax distribution). We investigate the fundamental properties of this model and its potential applications, particularly in handling heavy-tailed data. The proposed conditionally Gaussian hierarchical stochastic model provides a generalization of the Laplace probability distribution, which has already demonstrated its utility in various scientific disciplines. We present the model's basic properties and delve into related computational challenges, particularly those involving the inferential aspects of the model. The emergence of these distributions is explained as the limiting laws of suitably normalized random sums of independent and identically distributed (IID) random variables, where the number of terms follows a discrete Pareto distribution. We generalize this model by introducing a family of integer-valued random variables indexed by a parameter, which converge to infinity as the parameter becomes small. We further elaborate on constructing this family for a wide range of random variables with continuous distributions on the positive half-line. In the process, we introduce the concept of a "dual family", which encompasses both continuous and discrete distributions. The discrete members of the family are obtained by discretizing the continuous ones, and the continuous members are weak limits of the scaled discrete members. We also propose a new notion of discrete reciprocal distribution and discuss its connection to limiting distributions in the random summation scheme and mixtures of Gaussian distributions. Throughout the study, we provide several examples involving classical continuous and discrete distributions, as well as their new counterparts, to illustrate the theoretical constructions discussed. In particular, we introduce continuous analogues of well-known classical distributions like Poisson, binomial, and negative binomial, presenting basic facts related to these new models. Additionally, new results and generalizations concerning these distributions are presented, highlighting potential applications. This work also delves into computational issues that may arise when implementing these models practically, given the non-explicit nature of some of their basic characteristics. We shed light on the challenges and suggest potential solutions.In summary, this research presents a novel and comprehensive investigation into the location-scale mixtures of Gaussian distributions with Pareto Type II conditional mean and variance. The proposed model offers a powerful tool for handling heavy-tailed data and has potential applications in various scientific fields. The theoretical constructions and findings in the thesis contribute valuable insights to the understanding and application of these distributions

Innovative Ways of Gaining Access to Funds for SMEs Setups in Ghana

Small and Medium Enterprises contributes to the developments of private sectors, and the sustainable growth of any economy is very crucial. In both developing and developed economies, small and medium enterprises are considered as a backbone for economic growth and development. SME does do not only contribute to the growth of national GDP but also contributes to the reduction of the unemployment rate. In developing economies such as Ghana, SME’s provides 92% of registered companies, providing 85% of manufacturing employment and contributing 70% to the nations GDP. These clearly indicate a significant role SME’s play on the nation’s employment, income, economic growth and development.Despite all these significance, most SME’s in Ghana are challenged with access to finance, in setting up, expanding and sustainability of their businesses. The study found out that; these are commonly due to high interest and collateral rates by most financial institution, documentation requirements by financial institutions, long delay in gaining access to funds by credit institutions, capital cost and also unfavourable terms of credit repayment.  This study, therefore, focused on innovative ways of generating capital for small and medium enterprises from non-financial institutions.The study suggested alternative ways of SME’s gaining access to funds from non-financial institutions to enable SME’s benefit from, investing business smarts, networking opportunities, little or no contractual and collateral strings attached to loans, quick access to credit, and relative patience from investors regardless of their investments. Keywords: SME’s, Ghana, SME’s and economic development, Financial Institutions

A Comparative Study on Support Vector Machines

In this thesis, we study Support Vector Machines (SVMs) for binary classification. We review literature on SVMs and other classification methods. We perform simulations to compare kernel functions found in selected R packages and also investigate the variable selection property of penalized SVMs. We consider most linearly separable data set, mostly linearly non-separable data set, and linearly non-separable data set requiring nonlinear SVMs. In addition, traditional classification methods, including the Linear Discriminant Analysis, Quadratic Discriminant Analysis, K-Nearest Neighbors, and Logistic Regression, are also fit to the data sets and compared to the SVM models. The results of the simulation indicate that choosing a kernel function is key to obtaining a good fit to a particular data set. Moreover, in situations where nonlinear SVMs are not required (such as the linear separable data set) fitting nonlinear SVMs to a data set might likely result in overfitting. Finally, we apply SVMs and other classification techniques to Alzheimer's disease data

PHYSICAL EDUCATION CURRICULUM AND THE LEVEL OF PHYSICAL ACTIVITY OF BASIC SCHOOL CHILDREN IN GHANA

Purpose: This study sought to investigate the relationship between current physical education curriculum of basic schools and the level of physical activity of children in the Ga East Municipality of Ghana. Method: A total of 201 children from selected schools (4 with physical education curriculum [PE] and 4 without physical education curriculum [NPE]) were included in the study. A semi-structured questionnaire was used to collect information on socio-demographic characteristics and physical activity. Pearson’s Chi square test was used to evaluate the relationship between physical education curriculum and physical activity levels of school children. Results: Few of the children met the WHO recommendation for physical activity for the target age-group. The two groups did not differ with respect to the duration of physical activity of the children. Children attending public schools were four times more likely to engage in physical activities for at least 180 minutes per week compared to those in private schools. Conclusion: Current physical education curriculum was not related to the level of physical activity and nutritional status of basic school children in this study. PE lessons need to be restructured so as to meet the physical activity needs of children in basic schools.  Article visualizations

Interconnectedness of technology teachers’ perceptions of the design process to learner creativity

The design process (DP) is key to technology education and is considered as synonymous with problem solving, hence it undergirds all its learning aims and objectives. The Curriculum Assessment and Policy Statement (CAPS) document envisages that the design process will promote problem solving, critical thinking and creativity in learners. However, a paucity of empirical studies within the South African context illuminates the interconnectedness of DP to problem solving, critical thinking and creativity in learners for which the CAPS policy advocates. Further, there is a need to explore the interconnectedness of teachers’ perceptions of the DP, their enactment of the DP and its impact on learner creativity. This paper reports on a study that explored that interconnectedness and addressed the following research questions: What are grade 9 technology teachers’ perceptions of the design process? How do these perceptions relate to teachers’ reported enactment of the DP and creativity in learners? The conceptual framework used to model the interconnectedness that exists between teachers’ perceptions and reported enactment of the design process is Shulman’s pedagogical content knowledge model (PCK). This interpretivist study was located in the Umlazi district of KwaZulu-Natal. A case study design was used to collect qualitative data via an open-ended questionnaire and a semi-structured interview from 30 purposively selected technology teachers. Content analysis of data was undertaken in line with the conceptual framework. Our findings reflect that teachers’ perception and reported enactment of DP and the flexibility of the learning environment have an impact on opportunities for problem solving, critical thinking and creativity in learners. Our findings raise questions about the type of professional development teachers need to enact the envisaged goals of the CAPS document in respect of the DP in technology education

The Contribution of Fruit bats, Eidolon helvum, to biodiversity on the University of Energy and Natural Resources’ Campus, Sunyani, Ghana

The dispersal ability of straw coloured fruit bats (Eidolon helvum), was investigated on the University of Energy and Natural Resources (UENR) Campus in Sunyani from January 2013 to December 2014. A reconnaissance exercise was conducted in the UENR in order to stratify the campus into bat-occupied and unoccupied zones (strata) based on the presence or absence of roost trees occupied by bats. The Wildlife Sanctuary represented the main bat roost site (bat-occupied zone) whilst the rest of the campus constituted the unoccupied zone. Using 64 (4m x 4m) quadrats and 32 seed traps made from plastic sheets were set up randomly in the bat occupied areas. Seeds dispersed were collected on the seed traps and identified. The contribution of the dispersed seeds to the regeneration of the total plant population in the undergrowth wasestimated at 1.7%. Notable species which were dispersed by bats were Mallotus opposotifolius, (16.1%), Broussonetia papyrifera (10.6%), Ficus exasperate (6.6%), Solanum erianthum (6.2%) and Morus mesozygia (4.6%) of total seeds dispersed. These plants were found to have been introduced by E. helvum into the study area and are contributing to the ecological improvement by increasing biodiversity through regeneration. Key Words: Eidolon helvum, disperse, seeds, reconnaissanc

Strength prediction model for cement mortar made with waste LDPE plastic as fine aggregate

Abstract : Non-biodegradable aggregate prepared from low density polyethylene (LDPE) plastic was used as partial replacement for sand in cement mortar. Various volumetric fractions of 0, 5, 10, 20, 30, 40, 50, and 60% sand were replaced using ground LDPE waste plastic. Mortar mixtures of 1 : 3 cement to fine aggregate were prepared at various water /cement ratios of 0.45, 0.50, 0.55 and 0.60, then used to cast 50 mm cubes and 40 × 40 × 160 mm prisms. It was found that strength reduces significantly as the proportion of LDPE in mortar increases, however, mixtures containing 50 to 60% LDPE satisfy the strength criteria for masonry mortars. Based on experimental data, a model was proposed for predicting the compressive strength of mortars containing waste plastics. The model’s validation gave generally accurate predictions for the strengths of mortars made using different types of plastics

A review on re-activation of hardened cement paste and treatment of recycled aggregates

Abstract : The generation of construction and demolition waste (C&DW) worldwide keeps on escalating due to growth in infrastructure and the related refurbishment or replacement of existing structures. Numerous researches have been conducted towards utilizing C&DW materials for production of new concrete, from which it has been well-established that their use in concrete mixtures generally leads to inferior mechanical properties of the resulting concrete. As such, the general acceptance and conventional utilization of C&DW in the construction industry, is undermined. In this paper, the concept of triple layered interfacial transition zone (3ITZ) is suggested to be the main reason for the inferior mechanical properties exhibited by recycled aggregate concrete. The present paper reviewed past researches on re-activation of hydrated cement paste and on improving the quality of recycled aggregates by using different treatments. It is shown that a combination of mechanical grinding and thermal treatment at temperatures of 500 to 800oC, is an effective means of activating the cementitious properties of hardened cement paste. Adhered mortar removal and mortar fortification are the main approaches for enhancing the properties of recycled aggregates. Mechanical abrasion and/or thermal treatment at a temperature of 500oC, are the most effective techniques for improving the properties of recycled aggregates