Search results for "Normal Distribution"
showing 10 items of 135 documents
Finding condensed descriptions for multi-dimensional data.
1976
Abstract We describe two programs that may be used to find condensed descriptions for data available in a contingency table or in a covariance matrix in the case that these data follow a multinomial or a multivariate normal distribution, respectively. The programs perform a stepwise model search among multiplicative models by computing appropriate likelihood-ratio test statistics.
FABC: Retinal Vessel Segmentation Using AdaBoost
2010
This paper presents a method for automated vessel segmentation in retinal images. For each pixel in the field of view of the image, a 41-D feature vector is constructed, encoding information on the local intensity structure, spatial properties, and geometry at multiple scales. An AdaBoost classifier is trained on 789 914 gold standard examples of vessel and nonvessel pixels, then used for classifying previously unseen images. The algorithm was tested on the public digital retinal images for vessel extraction (DRIVE) set, frequently used in the literature and consisting of 40 manually labeled images with gold standard. Results were compared experimentally with those of eight algorithms as we…
Shaping ability of nickel-titanium rotary instruments in simulated S-shaped root canals.
2009
Objective The aim of this study was to compare the shaping ability of 4 nickel-titanium rotary techniques and 1 hand technique in simulated S-shaped curved root canals. Study design Seventy-five simulated double-curved resin root canals were divided into 5 groups (n = 15). The canals were compared at 12 different levels and at 3 different times: before preparation and after preparation to master apical 25 and 35. Data were statistically analyzed by performing 2-by-2 comparisons with the Tukey parametric test of variance analysis using a confidence interval of 95%. Results All of the 75 resin blocks presented transportation of the root canals by transforming the apical curvature into a strai…
Levy targeting and the principle of detailed balance
2011
We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …
Regular Minimality and Thurstonian-type modeling
2009
Abstract A Thurstonian-type model for pairwise comparisons is any model in which the response (e.g., “they are the same” or “they are different”) to two stimuli being compared depends, deterministically or probabilistically, on the realizations of two randomly varying representations (perceptual images) of these stimuli. The two perceptual images in such a model may be stochastically interdependent but each has to be selectively dependent on its stimulus. It has been previously shown that all possible discrimination probability functions for same–different comparisons can be generated by Thurstonian-type models of the simplest variety, with independent percepts and deterministic decision ru…
Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective …
2020
The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution w…
Weak versus strong dominance of shrinkage estimators
2021
We consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its eigenvalues. We prove that there are only two distinct eigenvalues and apply our findings to the James–Stein and the Thompson class of estimators. It turns out that the famous Stein paradox is no longer a paradox when we consider the whole mean squared error matrix rather than only its trace.
Estimating Engel curves under unit and item nonresponse
2010
SUMMARY This paper estimates food Engel curves using data from the first wave of the Survey on Health, Aging and Retirement in Europe (SHARE). Our statistical model simultaneously takes into account selectivity due to unit and item nonresponse, endogeneity problems, and issues related to flexible specification of the relationship of interest. We estimate both parametric and semiparametric specifications of the model. The parametric specification assumes that the unobservables in the model follow a multivariate Gaussian distribution, while the semiparametric specification avoids distributional assumptions about the unobservables. Copyright © 2011 John Wiley & Sons, Ltd.
Modeling Term Structure Dynamics in the Nordic Electricity Swap Market
2010
We analyze the daily returns of Nordic electricity swaps and identify significant risk premia in the short end of the market. On average, long positions in this part of the swap market yield negative returns. The daily returns are distinctively non-normal in terms of tail-fatness, but we find little evidence of asymmetry. We investigate if the flexible four-parameter class of normal inverse Gaussian (NIG) distributions can capture the observed stylized facts and find that this class of distributions offers a remarkably improved fit relative to the normal distribution. We also compare the fit with that of the four-parameter class of stable distributions; the NIG law outperforms the stable la…
On the world distribution of income
2015
In this paper we demonstrate that the size distribution of the world income may be reasonably approximated by a log-normal distribution rather then by a power law, as has previously been believed. This result has been shown to be quite persistent as we move from 1985 to 2011.