Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related to L'Hopital's monotone rule, can be used to obtain sharp bounds for cumulative d...
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Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related to L'Hopital's monotone rule, can be used to obtain sharp bounds for cumulative distribution functions. We consider the case of noncentral cumulative gamma and beta distributions. Three different types of sharp bounds for the noncentral gamma distributions (also called Marcum functions) are obtained in terms of modified Bessel functions and one additional type of function: a second modified Bessel function, two error functions or one incomplete gamma function. For the noncentral beta case the bounds are expressed in terms of Kummer functions and one additional Kummer function or an incomplete beta function. These bounds improve previous results with respect to their range of application and/or its sharpness. (C) 2015 Elsevier Inc. All rights reserved.
It is shown that Zolotarev's (1964) integral representation of the cumulativedistribution function (c.d.f.) of stable random variables and the IMSL subroutine DCADRE (for numerical integration ) provide a natural...
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It is shown that Zolotarev's (1964) integral representation of the cumulativedistribution function (c.d.f.) of stable random variables and the IMSL subroutine DCADRE (for numerical integration ) provide a natural and practically simple method for finding the values of c.d.f., the percentiles and the density function of such random variables. For symmetric stable random variables (r.v.'s ) Z∝, values of P∝(z) … P(0
In this paper, a novel model is presented to describe the composite mechanical properties degradation during cyclic loading. The model is based on cumulative distribution functions using. Weibull probability distribut...
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In this paper, a novel model is presented to describe the composite mechanical properties degradation during cyclic loading. The model is based on cumulative distribution functions using. Weibull probability distribution law and beta distribution are considered. The dependences of the fatigue sensitivity coefficient on the preliminary cyclic exposure are derived. The damage value function derivative using is proposed to define damage accumulation stages boundaries. Model parameters are obtained using experimental data. Determination coefficients are calculated. A high descriptive capability is noted. Rationality and expediency of using cumulative distribution functions as the approximation of experimental data on mechanical characteristics reduction after preliminary cyclic exposure is concluded.
In this note, we present an overlooked result derived from Fishburn's Convex Stochastic Dominance (CSD) (Fishburn (1974a;1974b). We demonstrate that CSD is a sufficient condition for establishing second-order stoc...
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In this note, we present an overlooked result derived from Fishburn's Convex Stochastic Dominance (CSD) (Fishburn (1974a;1974b). We demonstrate that CSD is a sufficient condition for establishing second-order stochastic dominance in the context of linear combinations of random variables. While this result may appear straightforward, to the best of our knowledge, it has not been explicitly presented as we have done in this work. Furthermore, the implications of this finding are extensive, as it can be applied to various areas of research, as we illustrate in this study.
作者：
Harrison, PUniv Leeds
Inst Microwaves & Photon Leeds LS2 9JT W Yorkshire England
There has been much speculation about the nature of the electron distributionfunctions in quantum cascade lasers, in particular: Are they non equilibrium and if so, to what extent? In order to address this, detailed ...
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There has been much speculation about the nature of the electron distributionfunctions in quantum cascade lasers, in particular: Are they non equilibrium and if so, to what extent? In order to address this, detailed calculations of the intersubband and intrasubband electron-longitudinal phonon and electron-electron scattering rates in a real GaAs/AlxGa1-xAs device design [Sirtori , Appl. Phys. Lett. 73, 3486 (1998)] are presented. The results suggest that two important conclusions relating to the electron distributionfunctions in the quantum well subbands can be drawn: the electron distributions in both the active region and the injector subbands are thermalized, i.e., they can be described by Fermi-Dirac distributionfunctions and furthermore all the electron distributions have the same electron temperature. (C) 1999 American Institute of Physics. [S0003- 6951(99)04344-2].
In this paper I examine graphical comparisons of one-dimensional (or marginal) distributionfunctions of alternative estimators. It is shown that areas under the c.d.f. (cumulativedistribution function) curve can be ...
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In this paper I examine graphical comparisons of one-dimensional (or marginal) distributionfunctions of alternative estimators. It is shown that areas under the c.d.f. (cumulativedistribution function) curve can be given a decision-theoretic interpretation as risk under a bounded absolute-error loss function. I also show that by a simple rescaling of the graph's axes, graphical areas are created which can be interpreted as risk under bounded squared-error loss. The bounded loss functions are applied to compare graphically and numerically the risk of exact distributions of the limited-information maximum likelihood and two-stage least-squares estimators in a simultaneous equations model.
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be ...
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Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multilevel method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://***/licenses/by/4.0/).
Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single componen...
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Two-dimensional hard disks are a fundamentally important many-body model system in classical statistical mechanics. Despite their significance, a comprehensive experimental data set for two-dimensional single component and binary hard disks is lacking. Here, we present a direct comparison between the full set of radial distributionfunctions and the contact values of a two-dimensional binary colloidal hard sphere model system and those calculated using fundamental measure theory. We find excellent quantitative agreement between our experimental data and theoretical predictions for both single component and binary hard disk systems. Our results provide a unique and fully quantitative mapping between experiments and theory, which is crucial in establishing the fundamental link between structure and dynamics in simple liquids and glass forming systems. (C) 2014 AIP Publishing LLC.
Linear properties of ring velocity distributionfunctions are investigated. The dispersion tensor in a form similar to the case of a Maxwellian distribution function, but for a general distribution function separable ...
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Linear properties of ring velocity distributionfunctions are investigated. The dispersion tensor in a form similar to the case of a Maxwellian distribution function, but for a general distribution function separable in velocities, is presented. Analytical forms of the dispersion tensor are derived for two cases of ring velocity distributionfunctions: one obtained from physical arguments and one for the usual, ad hoc ring distribution. The analytical expressions involve generalized hypergeometric, Kampe de Feriet functions of two arguments. For a set of plasma parameters, the two ring distributionfunctions are compared. At the parallel propagation with respect to the ambient magnetic field, the two ring distributions give the same results identical to the corresponding bi-Maxwellian distribution. At oblique propagation, the two ring distributions give similar results only for strong instabilities, whereas for weak growth rates their predictions are significantly different;the two ring distributions have different marginal stability conditions. (C) 2015 AIP Publishing LLC.
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