Search results for " Probability distribution"
showing 10 items of 100 documents
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
Response spectrum analysis of frame structures: reliability-based comparison between complete quadratic combination and damping-adjusted combination
2019
In the framework of seismic design of structures, response spectrum analysis (RSA) is the most commonly used approach in practice. The most popular combination rule is the complete quadratic combination (CQC) which is also prescribed by the most of seismic design codes and is based on the assumptions that the seismic acceleration is a white noise process and the peak factor ratios associated to the total and modal responses are unitary. Recently, the damping adjusted combination (DAC) rule has been developed for base-isolated structures to overcome the aforementioned simplified assumptions. Although it has been proved that the simplifications about peak factors lead to noticeable errors in …
Horizontal inequity comparisons
1998
In this paper, we expound the idea that horizontal inequity (HI) in different tax systems be compared by transplanting the HI from one tax system into the other, as a mapping between its pre- and post-tax living standard distributions, and then applying known results to compare the extent of association present in the two joint distributions. We make this idea operational by means of axioms which, we show, lead to an implementable procedure based on the `copula'. Statistical inference procedures are discussed, and illustrative empirical exercises are undertaken for the UK, Canadian and Israeli tax and benefit systems.
A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions
2008
Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of Gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on nite convolution of Gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function F (n) D and its con uent form (n) 2 , suitable for numerical integration; some graphics of the probability density function and distr…
Selectivity in Probabilistic Causality: Where Psychology Runs Into Quantum Physics
2011
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one determine, for each of the outputs, which of the inputs it is influenced by? The problem has applications ranging from modeling pairwise comparisons to reconstructing mental processing architectures to conjoint testing. A necessary and sufficient condition for a given pattern of selective influences is provided by the Joint Distribution Criterion, according to which the problem of "what influences what" is equivalent to that of the existence of a joint distr…
Joint Probability of Shape and Image Similarities to Retrieve 2D TRUS-MR Slice Correspondence for Prostate Biopsy
2012
International audience; This paper presents a novel method to identify the 2D axial Magnetic Resonance (MR) slice from a pre-acquired MR prostate volume that closely corresponds to the 2D axial Transrectal Ultrasound (TRUS) slice obtained during prostate biopsy. The method combines both shape and image intensity information. The segmented prostate contours in both the imaging modalities are described by shape-context representations and matched using the Chi-square distance. Normalized mutual information and correlation coefficient between the TRUS and MR slices are computed to find image similarities. Finally, the joint probability values comprising shape and image similarities are used in…
On the checking of g-coherence of conditional probability bounds
2003
We illustrate an approach to uncertain knowledge based on lower conditional probability bounds. We exploit the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), which is equivalent to the "avoiding uniform loss" property introduced by Walley for lower and upper probabilities. Based on the additive structure of random gains, we define suitable notions of non relevant gains and of basic sets of variables. Exploiting them, the linear systems in our algorithms can work with reduced sets of variables and/or constraints. In this paper, we illustrate the notions of non relevant gain and of basic set by examining several cases of imprecise assessments d…
Bayesian joint models for longitudinal and survival data
2020
This paper takes a quick look at Bayesian joint models (BJM) for longitudinal and survival data. A general formulation for BJM is examined in terms of the sampling distribution of the longitudinal and survival processes, the conditional distribution of the random effects and the prior distribution. Next a basic BJM defined in terms of a mixed linear model and a Cox survival regression models is discussed and some extensions and other Bayesian topics are briefly outlined.
Equivalence of the Pecka–Ponec Correlation Probability and the Statistical F Significance for MLR Models
2004
In an article of this journal Pecka and Ponec [J. Math. Chem. 27 (2000) 13] have proposed, by means of a probability calculation, a method to evaluate the statistical importance of correlations obtained from multilinear regression equations involving an arbitrary number of experimental points and parameters. Here, it is demonstrated how this probability exactly coincides with a more general concept: the confidence probability of an F distribution having the appropriate degrees of freedom.
Embedding Quantum into Classical: Contextualization vs Conditionalization
2014
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type ine…