Search results for "Normal Distribution"
showing 10 items of 135 documents
Non-Gaussian Distribution for Var Calculation: an Assessment for the Italian Market
2001
Abstract In this paper we compare different approaches to computing VaR (Value-at-Risk) for heavy tailed return series. Using data from the Italian market, we show that almost all the return series present statistically significant skewness and kurtosis. We implement (i) the stable models proposed by Rachev et al . (2000), (ii) an alternative to the Gaussian distributions based on a Generalized Error Distribution and (iii) a non-parametric model proposed by Li (1999). All the models are then submitted to backtest on out-of-sample data in order to assess their forecasting power. We observe that when the percentiles are low, all the models tested produce results that are dominant compared to …
Comparison of the Rain Flow Algorithm and the Spectral Method for Fatigue Life Determination Under Uniaxial and Multiaxial Random Loading
2008
This paper presents the strain energy density parameter used for fatigue life calculation under random loading by two methods. The first method is based on schematization of energy parameter histories with the rain flow algorithm. The other one is based on moments of the power spectral density function of the energy parameter. The experimental data of fatigue tests of 10HNAP steel under constant amplitude and random uniaxial loading with non-gaussion probability distribution, zero mean value, and wide-band frequency spectrum used for comparison of the rain flow algorithm and the spectral method gave satisfactory results. Next, histories of the random stress tensor with normal probability di…
Color image quality assessment measure using multivariate generalized Gaussian distribution
2014
This paper deals with color image quality assessment in the reduced-reference framework based on natural scenes statistics. In this context, we propose to model the statistics of the steer able pyramid coefficients by a Multivariate Generalized Gaussian distribution (MGGD). This model allows taking into account the high correlation between the components of the RGB color space. For each selected scale and orientation, we extract a parameter matrix from the three color components sub bands. In order to quantify the visual degradation, we use a closed-form of Kullback-Leibler Divergence (KLD) between two MGGDs. Using "TID 2008" benchmark, the proposed measure has been compared with the most i…
Unsupervised Anomaly and Change Detection With Multivariate Gaussianization
2022
Anomaly detection (AD) is a field of intense research in remote sensing (RS) image processing. Identifying low probability events in RS images is a challenging problem given the high dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While a plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary, especially now with the data deluge problem. In this article, we propose an unsupervised method for detecting anomalies and changes …
Kernel methods and their derivatives: Concept and perspectives for the earth system sciences.
2020
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However, kernel machines are still considered black-box models as the feature mapping is not directly accessible and difficult to interpret.The aim of this work is to show that it is indeed possible to interpret the functions learned by various kernel methods is intuitive despite their complexity. Specifically, we show that derivatives of these functions have a simple mathematical formulation, are easy to compute, and can be applied to many different problems. We n…
Randomized Rx For Target Detection
2018
This work tackles the target detection problem through the well-known global RX method. The RX method models the clutter as a multivariate Gaussian distribution, and has been extended to nonlinear distributions using kernel methods. While the kernel RX can cope with complex clutters, it requires a considerable amount of computational resources as the number of clutter pixels gets larger. Here we propose random Fourier features to approximate the Gaussian kernel in kernel RX and consequently our development keep the accuracy of the nonlinearity while reducing the computational cost which is now controlled by an hyperparameter. Results over both synthetic and real-world image target detection…
Using SMAA-2 method with dependent uncertainties for strategic forest planning
2006
Abstract Uncertainty included in forest variables is normally ignored in forest management planning. When the uncertainty is accounted for, it is typically assumed to be independently distributed for the criteria measurements of different alternatives. In forest management planning, the factors introducing the uncertainty can be classified into three main sources: the errors in the basic forestry data, the uncertainty of the (relative) future prices of timber, and the uncertainty in predicting the forest development. Due to the nature of these error sources, most of the involved uncertainties can be assumed to be positively correlated across the alternative management plans and/or criteria.…
Estimation of biogas produced by the landfill of Palermo, applying a Gaussian model
2008
Abstract In this work, a procedure is suggested to assess the rate of biogas emitted by the Bellolampo landfill (Palermo, Italy), starting from the data acquired by two of the stations for monitoring meteorological parameters and polluting gases. The data used refer to the period November 2005–July 2006. The methane concentration, measured in the CEP suburb of Palermo, has been analysed together with the meteorological data collected by the station situated inside the landfill area. In the present study, the methane has been chosen as a tracer of the atmospheric pollutants produced by the dump. The data used for assessing the biogas emission refer to night time periods characterized by weak…
SIMULATION EXPERIMENTS WITH MULTIPLE GROUP LINEAR AND QUADRATIC DISCRIMINANT ANALYSIS
1973
Summary A simulation program is described which can be performed to obtain estimates of the different types of misclassification probabilities for multiple group linear and quadratic discriminant analysis. The program can be used to study how these errors depend on sample sizes and the different parameters of the multivariate normal distribution. Examples for several simulation experiments are given and possible conclusions are discussed.
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
2015
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covar…