Search results for "Normal Distribution"
showing 10 items of 135 documents
On Mardia’s Tests of Multinormality
2004
Classical multivariate analysis is based on the assumption that the data come from a multivariate normal distribution. The tests of multinormality have therefore received very much attention. Several tests for assessing multinormality, among them Mardia’s popular multivariate skewness and kurtosis statistics, are based on standardized third and fourth moments. In Mardia’s construction of the affine invariant test statistics, the data vectors are first standardized using the sample mean vector and the sample covariance matrix. In this paper we investigate whether, in the test construction, it is advantageous to replace the regular sample mean vector and sample covariance matrix by their affi…
Statistical Techniques for Validation of Simulation and Analytic Stochastic Models
2014
In this paper, we consider the problem of statistical validation of multivariate stationary response simulation and analytic stochastic models of observed systems (say, transportation or service systems), which have p response variables. The problem is reduced to testing the equality of the mean vectors for two multivariate normal populations. Without assuming equality of the covariance matrices, it is referred to as the Behrens–Fisher problem. The main purpose of this paper is to bring to the attention of applied researchers the satisfactory tests that can be used for testing the equality of two normal mean vectors when the population covariance matrices are unknown and arbitrary. To illus…
Adaptive independent vector analysis for multi-subject complex-valued fMRI data.
2017
Abstract Background Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. New method To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV dis…
640-Slice CT Measurement of Superior Orbital Fissure as Gateway for Light into the Brain: Statistical Evaluation of Area and Distance.
2016
Objective Our aim was to provide normative data concerning superior orbital fissure area (SOFA), ocular skin and the substantia nigra (D-SS) and orbital fissure and the substantia nigra (D-SOF-S) distances by CT scan in adult Caucasian population. Methods The area of the superior orbital fissure (SOF), the distance between the ocular skin and the substantia nigra and the distance between the superior orbital fissure and the substantia nigra using CT and 3D-CT images. Results Normative data stratified for age and gender were obtained. The data here reported show that some degree of variability in SOFA, D-SS and D-SOF-S measurements can be observed healthy Caucasian subjects. Gender stratifie…
Infinitely Divisible Distributions
2020
For every n, the normal distribution with expectation μ and variance σ 2 is the nth convolution power of a probability measure (namely of the normal distribution with expectation μ/n and variance σ 2/n). This property is called infinite divisibility and is shared by other probability distributions such as the Poisson distribution and the Gamma distribution. In the first section, we study which probability measures on the real line are infinitely divisible and give an exhaustive description of this class of distributions by means of the Levy–Khinchin formula.
Brief Introduction to Probability Distributions
2014
There is a great deal of uncertainty in any project. That is, data is seldom absolutely reliable and exact, since there is never certainty about duration of tasks, price variations, effect on the environment, etc., to say nothing about those aspects which are external to the project and for which the project developer has no control, such as weather conditions, demand, stock fluctuations, inflation, supplier’s delays, etc. It is believed that many projects are not completed in time and finish with cost overrun, because in their preparation, data is taken as unquestionable, and then actual conditions show that it is not precisely the case. For this reason the uncertainty aspect has to be con…
Impact of Stock Price Jumps on Option Values
1999
Many empirical papers document the fact that the distribution of stock returns exhibits fatter tails than would be expected from a normal distribution. This might explain some of the pricing biases of the Black/Scholes model, which is] based on a normal return distribution. Given this result, alternative option pricing models should be based on one of the following three classes of return models: (1) a stationary process, such as a paretian stable or a student’s t-distribution, (2) a mixture of stationary distributions, such as two normal distributions with different means or variances, or a mixture of a diflusion and a pure jump process, or (3) a distribution such as a normal distribution …
Artificial driving cycles for the evaluation of energetic needs of electric vehicles
2012
International audience; This article presents a novel method to simulate artificial driving cycles that have the same significant characteristics as measured driving cycles. The driving cycles are based on only two different easily accessible parameters namely mean velocity and mean positive acceleration as well as their standard variations. Those parameters allow to adapt the driving cycles to different cycle types (urban, extra urban, highway), length and duration. Other than know drive cycle simulators, the approach is based on normal distribution of velocities and accelerations, thus needing to analyze only few cycles for the initialization.
Elliptically Symmetric Distributions: A Review of Achieved Results and Open Issues
2005
The spherically and elliptically symmetrical distributions are used in different statistical areas for different purposes such as the description of multivariate data, in order to find alternatives to the normal distribution in multinormality tests and in the creation of statistical models in which the usual assumption of normality is not realistic. Some achieved results, open issues and some proposals for their use in applications, especially in the financial area, are here presented.
Über eine methode zur bestimmung der intensität komplexer photopeaks
1966
Abstract Analysing photopeaks really occuring in γ-ray spectra their asymmetrical structure can easily be demonstrated. To describe the shape of photopeaks this study therefore recommends the use of empirical functions instead of the normal distribution function. It can be shown, that in a wide energy and intensity range photopeaks are exactly described by two empirical functions which are normalized with respect to the fractional peak height. Taking account of this fact, a new procedure is derived which allows the decomposition of overlapping photopeaks even in the case of small energy distance and unfavorable intensity ratio. The method applied to numerous examples under practical conditi…