Estimates of the Difference of Two Distribution Functions

2010 ◽  
pp. 29-36
Author(s):  
Zhengyan Lin ◽  
Zhidong Bai
Keyword(s):  
Distribution Functions ◽  
The Difference

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

Phenylalanyl-tRNA Synthetase from Baker'Yeast: Structural Organization of the Enzyme and Its Complex with tRNAPhe as Determined by X-Ray Small-Angle Scattering

1979 ◽  
Vol 34 (1-2) ◽  
pp. 20-26 ◽  
Author(s):  
Ingrid Pilz ◽  
Karin Goral ◽  
Friedrich v. d. Haar
Keyword(s):  
Molecular Weight ◽  
Small Angle ◽  
Quaternary Structure ◽  
Trna Synthetase ◽  
Distribution Functions ◽  
Maximum Diameter ◽  
Radius Of Gyration ◽  
X Ray ◽  
Angle Scattering ◽  
The Difference

Abstract The quaternary structure of the phenylalanyl-tRNA synthetase and its complex with tRNAPhe was studied in dilute solutions by small angle X-ray scattering. For the free synthetase the radius of gyration was determined as 5.5 nm, the volume 523 nm3, the maximum diameter 17.5 nm and the molecular weight as 260 000 using an isopotential specific volume of 0.735. The overall shape could be best approximated by a flat cylinder with dimensions 18.2 nm X 11.5 nm X 4 nm ; the loose structure was approximated by building up the cylinder by spheres (diameter 4.2 nm).The corresponding parameters of the enzyme tRNA complex were the following: radius of gyration 5.9 nm, volume 543 nm 3, maximum diameter 21 nm and molecular weight 290 000. These parameters suggest an 1:1 complex, whereby it must be assumed that the tRNA molecule is attached in the extension of the longer axis. From the difference in the distance distribution functions of the free enzyme and the complex it is evident that we have to assume a change of conformation (contraction) of the enzyme upon the binding of the specific tRNA.

scholarly journals Modeling of public transport waiting time indicator for the transport network of a large city

2018 ◽  
Vol 224 ◽  
pp. 04018 ◽  
Author(s):  
Olga Lebedeva ◽  
Marina Kripak
Keyword(s):  
Waiting Time ◽  
Large City ◽  
Distribution Functions ◽  
Weibull Function ◽  
Explanatory Variables ◽  
Transport Services ◽  
Time Period ◽  
Bus Stops ◽  
The Difference ◽  
Expected Waiting Time

The need to develop and improve public passenger transport in major cities was noted. It was reflected that waiting time at bus stops is one of the factors that have a big impact on the passenger quality assessment of transport services. The results of an empirical study of the actual and anticipated waiting time at bus stops were given. It was noted that the reliability functions were used in the field of ride duration modeling, traffic restoration time after an accident, and length of making the decision to travel. The waiting time distribution functions using the lognormal function and the Weibull function were chosen. The results of modeling were objective, the dependent variables in it were the expected waiting time of passengers and the difference between the anticipated and the actual waiting time. The explanatory variables were sex, age, time period, purpose of the trip and the actual waiting time. The results of the research showed that the age, purpose of the trip and the time period influence the waiting time perception, prolong it and lead to its reassessment.

scholarly journals Dynamical Age Determination of Open Clusters

1980 ◽  
Vol 85 ◽  
pp. 221-222
Author(s):  
M. Buchholz ◽  
Th. Schmidt-Kaler
Keyword(s):  
Age Determination ◽  
Dynamical Theory ◽  
Distribution Functions ◽  
Open Clusters ◽  
Kolmogorov Smirnov ◽  
The Difference ◽  
Absolute Age ◽  
Image Position ◽  
Smirnov Test

The radial mass distribution (obtained by counting stars in strips) of the real cluster is compared successively to the distribution functions of a simulated cluster of 100 stars, each of which corresponds to a certain dynamical age, Tdyn, The value of Tdyn, belonging to the function most similar to the observed one is taken to be the dynamical age of the cluster. The radius is given in units of R1/2 (sphere containing half of the total mass); this unit is nearly time-independent. The difference between the distribution functions is measured by the maximum Δmax of the Kolmogorov-Smirnov test which is free from assumptions on the form of the distributions. The minimum in the plot Δmax vs Tdyn, indicates the age of the cluster. It is then converted into an absolute age, Tabs (in years), by The error due to the dynamical theory (limited number of distribution functions, etc.) is estimated at 12%, the error due to the uncertainty of diameter and mass of the cluster is about 30%. Unreliable results were obtained in case of strongly inhomogeneous reddening of the cluster. As an example, the plot of the test values for NGC 457 is given in Figure 1.

scholarly journals Influence of Topology and Brønsted Acid Site Presence on Methanol Diffusion in Zeolites Beta and MFI

Catalysts ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1342
Author(s):  
Cecil Botchway ◽  
Richard Tia ◽  
Evans Adei ◽  
Alexander O’Malley ◽  
Nelson Dzade ◽  
...  
Keyword(s):  
Molecular Diffusion ◽  
Catalytic Performance ◽  
Acid Sites ◽  
Distribution Functions ◽  
Bronsted Acid ◽  
Brønsted Acid ◽  
A Value ◽  
Methanol To Hydrocarbons ◽  
Brönsted Acid ◽  
The Difference

Detailed insight into molecular diffusion in zeolite frameworks is crucial for the analysis of the factors governing their catalytic performance in methanol-to-hydrocarbons (MTH) reactions. In this work, we present a molecular dynamics study of the diffusion of methanol in all-silica and acidic zeolite MFI and Beta frameworks over the range of temperatures 373–473 K. Owing to the difference in pore dimensions, methanol diffusion is more hindered in H-MFI, with diffusion coefficients that do not exceed 10 × 10−10 m2s−1. In comparison, H-Beta shows diffusivities that are one to two orders of magnitude larger. Consequently, the activation energy of translational diffusion can reach 16 kJ·mol−1 in H-MFI, depending on the molecular loading, against a value for H-Beta that remains between 6 and 8 kJ·mol−1. The analysis of the radial distribution functions and the residence time at the Brønsted acid sites shows a greater probability for methylation of the framework in the MFI structure compared to zeolite Beta, with the latter displaying a higher prevalence for methanol clustering. These results contribute to the understanding of the differences in catalytic performance of zeolites with varying micropore dimensions in MTH reactions.

The statistics of stiff chain molecules I. The particle scattering factor

1970 ◽  
Vol 316 (1525) ◽  
pp. 185-199 ◽  
Keyword(s):  
Distribution Functions ◽  
Chain Model ◽  
Particle Scattering ◽  
Hindered Rotation ◽  
Chain Molecules ◽  
Chain Stiffness ◽  
Angle Scattering ◽  
Analytic Expressions ◽  
Scattering Factor ◽  
The Difference

Analytic expressions for the particle scattering factor of stiff chains have been derived, both for the wormlike and a discrete chain model with an axial symmetric potential of hindered rotation. The angular distribution functions agree well with the results of Monte Carlo calculations by Heine, Kratky & Roeppert (1962), if the chains are longer than five persistence lengths. The particle scattering factor of short chains can be well represented by the simple Guinier approximation. A transition point from the behaviour of a coil to that of the rod-like short chain sections has been determined by graphical extrapolation and appears at X a = 2.87 ± 0.05. The difference between the wormlike and the discrete chain models turned out to be smaller than 14% even for an alkane type chain with free rotation of the chain elements and decreases with increasing chain stiffness. The influence of the cross-section has been taken into account by representing the chain by a pearl necklace. Comparison with X -ray small angle scattering measurements of a cellulosetricarbanilate reveals close similarities between calculated and experimental curves.

scholarly journals The difference between the product and the convolution product of distribution functions in Rn

2011 ◽  
Vol 89 (103) ◽  
pp. 19-36 ◽  
Author(s):  
E. Omey ◽  
R. Vesilo
Keyword(s):  
Distribution Function ◽  
Distribution Functions ◽  
Convolution Product ◽  
Random Vectors ◽  
The Difference

Assume that X? and Y? are independent, nonnegative d-dimensional random vectors with distribution function (d.f.) F(x?) and G(x?), respectively. We are interested in estimates for the difference between the product and the convolution product of F and G, i.e., D(x?) = F(x?)G(x?) ? F ? G(x?). Related to D(x?) is the difference R(x?) between the tail of the convolution and the sum of the tails: R(x?) = (1 ? F ? G(x?))?(1 ? F(x?) + 1 ? G(x?)). We obtain asymptotic inequalities and asymptotic equalities for D(x?) and R(x?). The results are multivariate analogues of univariate results obtained by several authors before.

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