			Home About us Contact

Triangular Distribution (triangular + distribution)

Distribution by Scientific Domains

Mathematics and Statistics	66%

Selected Abstracts

Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions

BIOMETRICS, Issue 2 2001
F. Perron
Summary. Nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical Bayesian context, using the entire posterior distribution rather than particular expectations, increases its flexibility. In this article, the focus is on nonparametric estimation through a mixture of triangular distributions. The optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived. Although our approach is more widely applicable, we focus for simplicity on estimation of a monotone nondecreasing regression on [0, 1] with additive error, effectively approximating the function of interest by a function having a piecewise linear derivative. Computationally accessible methods of estimation are described through an amalgamation of existing Markov chain Monte Carlo algorithms. Simulations and examples illustrate the approach. [source]

Simplified inelastic seismic analysis of base-isolated structures using the N2 method

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2010
Vojko Kilar
Abstract In the paper a simplified nonlinear method has been applied to the analysis of base-isolated structures. In the first part, a three-linear idealization of the capacity curve is proposed. The initial stiffness is defined based on the first yielding point in the superstructure, whereas the secondary slope depends on the failure mechanism of the superstructure. A consequence is a much more pronounced secondary slope, which does not correspond to the presumptions used in the originally proposed N2 method. A parametric nonlinear dynamic study of single degree of freedom systems with different hardening slopes and damping has been performed for an ensemble of seven EC8 spectrum-compatible artificial accelerograms. It was concluded that, in the long-period range, the equal displacement rule could be assumed also for the proposed systems with non-zero post-yield stiffness. In the second part, the proposed idealization was used for the analysis of isolated RC frame buildings that were isolated with different (lead) rubber-bearing isolation systems. The stiffness of the isolators was selected for three different protection levels and for three different ground motion intensities, which have resulted in elastic as well as moderately and fully damaged superstructure performance levels. Three different lateral load distributions were investigated. It was observed that a triangular distribution, with an additional force at the base, works best in the majority of practical cases. It was concluded that the N2 method can, in general, provide a reasonably accurate prediction of the actual top displacement, as well as of the expected damage to the superstructure. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Predictive distributions in risk analysis and estimation for the triangular distribution

ENVIRONMETRICS, Issue 7 2001
Yongsung Joo
Abstract Many Monte Carlo simulation studies have been done in the field of risk analysis. This article demonstrates the importance of using predictive distributions (the estimated distributions of the explanatory variable accounting for uncertainty in point estimation of parameters) in the simulations. We explore different types of predictive distributions for the normal distribution, the lognormal distribution and the triangular distribution. The triangular distribution poses particular problems, and we found that estimation using quantile least squares was preferable to maximum likelihood. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Biodiversity conservation in Mediterranean and Black Sea lagoons: a trait-oriented approach to benthic invertebrate guilds

AQUATIC CONSERVATION: MARINE AND FRESHWATER ECOSYSTEMS, Issue S1 2008
A. Basset
Abstract 1. The extent to which conservation of biodiversity enforces the protection of ecosystem functioning, goods and services is a key issue in conservation ecology. 2. In order to address this conservation issue, this work focused on community organization, linking community structure, as described both in taxonomic and functional terms, to community functioning and ecosystem processes. 3. Body size is an individual functional trait that is deterministically related to components of ecosystem functioning such as population dynamics and energy flow, and which determines components of community structure. Since body size is an individual trait that reflects numerous factors, it is also exposed to trait selection and the niche filtering underlying the community. 4. An analysis of the relevance of body size to community organization in transitional water ecosystems in the eastern Mediterranean and Black Sea regions is presented, based on field research conducted on a sample of 15 transitional water ecosystems. 5. 250 taxa were identified, clumped in five orders of magnitude of body size. All body size patterns showed triangular distributions with an optimal size range of 0.13 mg to 1.0 mg individual body mass. 6. Deterministic components of size structure were emphasized and a hierarchical organization with dominance of large sizes was demonstrated by the slopes of the body size-abundance distributions, consistently larger than the EER threshold (b=,0.75), and by the direct relationship of energy use to body size for most of the body size range. 7. Consistent variations of body size-related descriptors were observed on three main gradients of environmental stress: eutrophication, confinement and metal pollution. 8. The results support the relevance of constraints imposed by individual body size on community organization in transitional water ecosystems and the adequacy of size patterns as an indicator for ecological conservation of these fragile ecosystems. Copyright © 2008 John Wiley & Sons, Ltd. [source]