On Multivariate Normal Probability Distributions

2013 ◽  
pp. 295-300
Author(s):  
FRANÇOIS N. FRENKIEL ◽  
JAMES W. FOLLIN
Keyword(s):  
Probability Distributions ◽  
Multivariate Normal ◽  
Normal Probability

scholarly journals Computing Spatiotemporal Accessibility to Urban Opportunities: A Reliable Space-Time Prism Approach in Uncertain Urban Networks

Computation ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 51
Author(s):  
Alireza Sahebgharani ◽  
Mahmoud Mohammadi ◽  
Hossein Haghshenas
Keyword(s):  
Travel Time ◽  
Traffic Congestion ◽  
Probability Distributions ◽  
Space Time ◽  
Unified Framework ◽  
Urban Networks ◽  
Street Networks ◽  
Normal Probability ◽  
Significant Difference ◽  
Temporal Dimensions

Space-time prism (STP) is a comprehensive and powerful model for computing accessibility to urban opportunities. Despite other types of accessibility measures, STP models capture spatial and temporal dimensions in a unified framework. Classical STPs assume that travel time in street networks is a deterministic and fixed variable. However, this assumption is in contradiction with the uncertain nature of travel time taking place due to fluctuations and traffic congestion. In addition, travel time in street networks mostly follows non-normal probability distributions which are not modeled in the structure of classical STPs. Neglecting travel time uncertainty and disregarding different types of probability distributions cause unrealistic accessibility values in STP-based metrics. In this way, this paper proposes a spatiotemporal accessibility model by extending classical STPs to non-normal stochastic urban networks and blending this modified STP with the attractiveness of urban opportunities. The elaborated model was applied on the city of Isfahan to assess the accessibility of its traffic analysis zones (TAZs) to Kowsar discount retail markets. A significant difference was found between the results of accessibility values in normally and non-normally distributed networks. In addition, the results show that the northern TAZs had larger accessibility level compared to the southern ones.

scholarly journals Hyperspectral Anomaly Detection: Comparative Evaluation in Scenes with Diverse Complexity

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Dirk Borghys ◽  
Ingebjørg Kåsen ◽  
Véronique Achard ◽  
Christiaan Perneel
Keyword(s):  
Anomaly Detection ◽  
Hyperspectral Data ◽  
Data Cube ◽  
Detection Methods ◽  
Multivariate Normal ◽  
Normal Probability ◽  
Local Methods ◽  
Anomaly Detector ◽  
The Difference ◽  
Rx Detector

Anomaly detection (AD) in hyperspectral data has received a lot of attention for various applications. The aim of anomaly detection is to detect pixels in the hyperspectral data cube whose spectra differ significantly from the background spectra. Many anomaly detectors have been proposed in the literature. They differ in the way the background is characterized and in the method used for determining the difference between the current pixel and the background. The most well-known anomaly detector is the RX detector that calculates the Mahalanobis distance between the pixel under test (PUT) and the background. Global RX characterizes the background of the complete scene by a single multivariate normal probability density function. In many cases, this model is not appropriate for describing the background. For that reason a variety of other anomaly detection methods have been developed. This paper examines three classes of anomaly detectors: subspace methods, local methods, and segmentation-based methods. Representative examples of each class are chosen and applied on a set of hyperspectral data with diverse complexity. The results are evaluated and compared.

Textural properties of regoliths on vegetated steep slopes in upland regions, Scotland

1986 ◽  
Vol 77 (3) ◽  
pp. 241-250 ◽  
Author(s):  
J. L. Innes
Keyword(s):  
Particle Size ◽  
Early Stage ◽  
Probability Distributions ◽  
Textural Properties ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Normal Probability ◽  
Log Normal ◽  
Steep Slopes

ABSTRACTThe textural properties of many sediments provide a good indication of their provenance, but surprisingly little information is available on the transitional stages between the breakdown of a rock and the incorporation of the material into a fluvial sediment. These transitional stages are important as certain fractions (particularly the finer ones) may be selectively removed. Regoliths developed on steep slopes represent an early stage in the debris cascade and they are here examined in detail to assess the role of parent lithology on the textural properties of the regolith. There are substantial variations between lithologies, although the majority of regoliths are dominated by coarser fractions and are poorly sorted. Most particle size distributions show some degree of fit to both log-normal probability distributions and Rosin distributions. Differences from these can be ascribed to the processes operating on steep slopes, particularly the influx of sand- and silt-sized material by colluvial processes and the removal of clay-sized material by leaching. The regoliths form a distinct facies type which may be recognisable in the geological record.

scholarly journals Application of five continuous distributions and evaluation of wind potential at five stations using normal distribution

2020 ◽  
pp. 014459872093937
Author(s):  
Muhammad Sumair ◽  
Tauseef Aized ◽  
Syed Asad Raza Gardezi ◽  
Muhammad Mahmood Aslam Bhutta ◽  
Syed Muhammad Sohail Rehman ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Normal Distribution ◽  
Probability Distributions ◽  
Evaluation Criteria ◽  
Energy Generation ◽  
Rayleigh Distribution ◽  
Normal Probability ◽  
Wind Potential ◽  
Chi Squared ◽  
Best Fit

Application of Weibull distribution in a generalized way to estimate wind potential cannot always be advisable. The novelty of this work is to estimate wind potential using Normal probability density function. A comparison of five probability distributions namely Normal, Gamma, Chi-Squared, Weibull, and Rayleigh was done using three performance evaluation criteria. Four years (2015–2018) hourly wind data at 50 m height at five stations near the coastline of Pakistan was used. It was found that normal distribution gives the best fit at each of these stations and against each evaluation criterion followed by Weibull distribution while Rayleigh distribution gives the poorest fit. Further energy generation by fifteen turbine models was calculated and GE 45.7 was found the best in terms of amount of energy generation and capacity factors while Vestas V42 shows the worst. However, GE/1.5 SL is the most economical while Vestas V63 is the least. Among five locations, Shahbandar is the best potential site while Manora is the least.

scholarly journals On spherical Monte Carlo simulations for multivariate normal probabilities

2015 ◽  
Vol 47 (03) ◽  
pp. 817-836 ◽  
Author(s):  
Huei-Wen Teng ◽  
Ming-Hsuan Kang ◽  
Cheng-Der Fuh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Multivariate Normal ◽  
Integration Rule ◽  
Radial Integral ◽  
Normal Probability ◽  
Antithetic Variates ◽  
Number Problem ◽  
Spherical Transformation

The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.

scholarly journals Quantification of Scenario Distance within Generic WINNER Channel Model

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Milan Narandžić ◽  
Christian Schneider ◽  
Wim Kotterman ◽  
Reiner S. Thomä
Keyword(s):  
Channel Model ◽  
Probability Distributions ◽  
Correlation Coefficients ◽  
Mimo Channel ◽  
Normal Probability ◽  
Leibler Divergence ◽  
Suitable Space ◽  
Indoor Scenarios ◽  
Stochastic Properties

Starting from the premise that stochastic properties of a radio environment can be abstracted by defining scenarios, a generic MIMO channel model is built by the WINNER project. The parameter space of the WINNER model is, among others, described by normal probability distributions and correlation coefficients that provide a suitable space for scenario comparison. The possibility to quantify the distance between reference scenarios and measurements enables objective comparison and classification of measurements into scenario classes. In this paper we approximate the WINNER scenarios with multivariate normal distributions and then use the mean Kullback-Leibler divergence to quantify their divergence. The results show that the WINNER scenario groups (A, B, C, and D) or propagation classes (LoS, OLoS, and NLoS) do not necessarily ensure minimum separation within the groups/classes. Instead, the following grouping minimizes intragroup distances: (i) indoor-to-outdoor and outdoor-to-indoor scenarios (A2, B4, and C4), (ii) macrocell configurations for suburban, urban, and rural scenarios (C1, C2, and D1), and (iii) indoor/hotspot/microcellular scenarios (A1, B3, and B1). The computation of the divergence between Ilmenau and Dresden measurements and WINNER scenarios confirms that the parameters of the C2 scenario are a proper reference for a large variety of urban macrocell environments.

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