Abstract: We use the skew distribution generation procedure proposed by Azzalini [Scand. J. Stat., 1985, 12, 171–178] to create three new probability distribution functions. These models make use of normal, student-t and generalized logistic distribution, see Rathie and Swamee [Technical Research Report No. 07/2006. Department of Statistics, University of Brasilia: Brasilia, Brazil, 2006]. Expressions for the moments about origin are derived. Graphical illustrations are also provided. The distributions derived in this paper can be seen as generalizations of the distributions given by Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. Applications with unimodal and bimodal data are given to illustrate the applicability of the results derived in this paper. The applications include the analysis of the following data sets: (a) spending on public education in various countries in 2003; (b) total expenditure on health in 2009 in various countries and (c) waiting time between eruptions of the Old Faithful Geyser in the Yellow Stone National Park, Wyoming, USA. We compare the fit of the distributions introduced in this paper with the distributions given by Nadarajah and Kotz [Acta Appl. Math., 2006, 91, 1–37]. The results show that our distributions, in general, fit better the data sets. The general R codes for fitting the distributions introduced in this paper are given in Appendix A.
Abstract: The Lvov-Warsaw School (L-WS) was the most important movement in the history of Polish philosophy, and certainly prominent in the general history of philosophy, and 20th century logics and mathematics in particular.[...]
Abstract: Data Farming is a process that has been developed to support decision-makers by answering questions that are not currently addressed. Data farming uses an inter-disciplinary approach that includes modeling and simulation, high performance computing, and statistical analysis to examine questions of interest with a large number of alternatives. Data farming allows for the examination of uncertain events with numerous possible outcomes and provides the capability of executing enough experiments so that both overall and unexpected results may be captured and examined for insights. Harnessing the power of data farming to apply it to our questions is essential to providing support not currently available to decision-makers. This support is critically needed in answering questions inherent in the scenarios we expect to confront in the future as the challenges our forces face become more complex and uncertain. This article was created on the basis of work conducted by Task Group MSG-088 “Data Farming in Support of NATO”, which is being applied in MSG-124 “Developing Actionable Data Farming Decision Support for NATO” of the Science and Technology Organization, North Atlantic Treaty Organization (STO NATO).
Abstract: In agent based models, the agents are usually platforms (individual soldiers, tanks, helicopters, etc.), not military units. In the Sandis software, the agents can be platoon size units. As there are about 30 soldiers in a platoon, there is a need for strength distribution in simulations. The contribution of this paper is a conceptual model of the platoon level agent, the needed mathematical models and concepts, and references earlier studies of how simulations have been conducted in a data farming environment with platoon/squad size unit agents with strength distribution.
Abstract: In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then a series representation and asymptotics of the fundamental solution are discussed. The fundamental solution is interpreted as a probability density function and its entropy in the Shannon sense is calculated. The entropy production rate of the stochastic process governed by the α-fractional diffusion equation is shown to be equal to one of the conventional diffusion equation.
Abstract: A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g., Buchholz-Wichmann nuclearity). We propose instead to use a modular ℓp -condition, which is an extension of a strengthened modular nuclearity condition to generally covariant theories. The modular nuclearity condition was previously introduced in Minkowski space, where it played an important role in constructive two dimensional algebraic QFT’s. We show that our generally covariant extension of this condition makes sense for a vast range of theories, and that it behaves well under causal propagation and taking mixtures. In addition we show that our modular ℓp -condition holds for every quasi-free Hadamard state of a free scalar quantum field (regardless of mass or scalar curvature coupling). However, our condition is not equivalent to the Hadamard condition.