The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. T...
详细信息
The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non-centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schlafli and Abrahamson are extended to show that any non-centred orthant probability can be expressed as differences between at most (m - 1)! non-centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.
We investigate energy transfer of air-water interactions and develop a numerical method that captures its temporal variability and generates and tracks the short waves that form in the water surface as a result of the...
详细信息
We investigate energy transfer of air-water interactions and develop a numerical method that captures its temporal variability and generates and tracks the short waves that form in the water surface as a result of the air-water turbulence. We solve a novel system of balance equations derived from the Navier-Stokes equations known as moment field equations. The main advantage of our approach is that we do not assume a priori that the stochastic random variables that quantify the turbulent energy transfer between air and water are Gaussian. We generate non-conservative multifractal measures of turbulent energy transfer using a recursive integration process and a self-affine velocity kernel. The kernel exactly satisfies the (duration limited) kinetic equation for waves as well as invariant scaling properties of the Navier-Stokes equations. This allows us to derive source terms for the moment field equations using a turbulent diffusion operator. The operator quantifies energy transfer along a space time path associated with pressure instabilities in the air-sea interface and transfers the statistical shape (or fractal dimension) of the atmosphere to the wind-sea. Because we use observational data to begin the recursive integration process, the ocean-atmosphere interaction is inherently built into the model. Numerical results from application of our methods to air-sea turbulence off the coast of New Jersey and New York indicate that our methods produce measures of turbulent energy transfer that match theory and observation, and, correspondingly, significant wave heights and average wave periods predicted by our model qualitatively match buoy data.
In this article, a procedure for comparisons between k (k >= 3) successive populations with respect to the variance is proposed when it is reasonable to assume that variances satisfy simple ordering. Critical const...
详细信息
In this article, a procedure for comparisons between k (k >= 3) successive populations with respect to the variance is proposed when it is reasonable to assume that variances satisfy simple ordering. Critical constants required for the implementation of the proposed procedure are computed numerically and selected values of the computed critical constants are tabulated. The proposed procedure for normal distribution is extended for making comparisons between successive exponential populations with respect to scale parameter. A comparison between the proposed procedure and its existing competitor procedures is carried out, using Monte Carlo simulation. Finally, a numerical example is given to illustrate the proposed procedure.
A new procedure for testing the H-0: mu(1)=mu(k) against the alternative H-u:mu(1) >= ...>= mu(r) <= ...<= mu(k) with at least one strict inequality, where mu(i) is the location parameter of the ith two-pa...
详细信息
A new procedure for testing the H-0: mu(1)=mu(k) against the alternative H-u:mu(1) >= ...>= mu(r) <= ...<= mu(k) with at least one strict inequality, where mu(i) is the location parameter of the ith two-parameter exponential distribution, i = 1,...,k, is proposed. Exact critical constants are computed using a recursive integration algorithm. Tables containing these critical constants are provided to facilitate the implementation of the proposed test procedure. Simultaneous confidence intervals for certain contrasts of the location parameters are derived by inverting the proposed test statistic. In comparison to existing tests, it is shown, by a simulation study, that the new test statistic is more powerful in detecting U-shaped alternatives when the samples are derived from exponential distributions. As an extension, the use of the critical constants for comparing Pareto distribution parameters is discussed.
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a...
详细信息
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings , motivated by models in lattice gauge theory from quantum field theory. A novel element of this work is the potential benefit in using lattice cubature rules. The group structure within lattice rules combined with the special structure in the physics integrands may allow efficient computations based on Fast Fourier Transforms. Applications to the quantum mechanical rotor and compact U(1) lattice gauge theory in two and three dimensions are considered. (C) 2021 Elsevier Inc. All rights reserved.
This paper considers the evaluation of probabilities which are defined by a set of linear inequalities of a trivariate normal distribution. It is shown that these probabilities can be evaluated by a one-dimensional nu...
详细信息
This paper considers the evaluation of probabilities which are defined by a set of linear inequalities of a trivariate normal distribution. It is shown that these probabilities can be evaluated by a one-dimensional numerical integration. The trivariate normal distribution can have any covariance matrix and any mean vector, and the probability can be defined by any number of one-sided and two-sided linear inequalities. This affords a practical and efficient method for the calculation of these probabilities which is superior to basic simulation methods. An application of this method to the analysis of pairwise comparisons of four treatment effects is discussed.
We consider the problem of evaluation of the probability that all elements of a multivariate normally distributed vector have non-negative coordinates;this probability is called the non-centred orthant probability. Th...
详细信息
We consider the problem of evaluation of the probability that all elements of a multivariate normally distributed vector have non-negative coordinates;this probability is called the non-centred orthant probability. The necessity for the evaluation of this probability arises frequently in statistics. The probability is defined by the integral of the probability density function. However, direct numerical integration is not practical. In this article, a method is proposed for the computation of the probability. The method involves the evaluation of a measure on a unit sphere surface in p-dimensional space that satisfies conditions derived from a covariance matrix. The required computational time for the p-dimensional problem is proportional to p(2).2(p-1), and it increases at a rate that is lower than that in the case of the existing method.
暂无评论