Exact distribution of a linear combination of a variable and order statistics from the other two variables of a trivariate elliptical random vector as a mixture of skew-elliptical distributions

2009 ◽  
Vol 6 (6) ◽  
pp. 634-644 ◽  
Author(s):  
A. Jamalizadeh ◽  
H. Mahmoodian ◽  
N. Balakrishnan
Keyword(s):  
Order Statistics ◽  
Linear Combination ◽  
Random Vector ◽  
Exact Distribution ◽  
The Other ◽  
Elliptical Distributions

scholarly journals On the Recurrence Properties of Narayana’s Cows Sequence

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 149
Author(s):  
Xin Lin
Keyword(s):  
Linear Combination ◽  
The Other ◽  
Other Hand ◽  
Computation Formula ◽  
The One

In this paper, we consider the recurrence properties of two generalized forms of Narayana’s cows sequence. On the one hand, we study Narayana’s cows sequence at negative indices and express it as the linear combination of the sequence at positive indices. On the other hand, we study the convolved Narayana number and obtain a computation formula for it.

Multivariate extremes, aggregation and dependence in elliptical distributions

2002 ◽  
Vol 34 (03) ◽  
pp. 587-608 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Random Vector ◽  
Positive Constant ◽  
Tail Dependence ◽  
Constant Factor ◽  
Dispersion Matrix ◽  
Elliptical Distributions ◽  
Spectral Measures ◽  
Lower Tail ◽  
Explicit Formulae ◽  
Dependence Properties

In this paper, we clarify dependence properties of elliptical distributions by deriving general but explicit formulae for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall's tau is invariant in the class of elliptical distributions with continuous marginals and a fixed dispersion matrix, we show that this is not true for Spearman's rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts.

A modified Runge-Kutta method

SIMULATION ◽  
1968 ◽  
Vol 10 (5) ◽  
pp. 221-223 ◽  
Author(s):  
A.S. Chai
Keyword(s):  
Error Estimate ◽  
Linear Combination ◽  
Experimental Results ◽  
The Other ◽  
New Method ◽  
Kutta Method ◽  
Starting Values ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
A Minor

It is possible to replace k2 in a 4th-order Runge-Kutta for mula (also Nth-order 3 ≤ N ≤ 5) by a linear combination of k1 and the ki's in the last step, using the same procedure for computing the other ki's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values. Experimental results are shown in verification of the for mula.

scholarly journals On a construction of multivariate distributions given some multidimensional marginals

2019 ◽  
Vol 51 (2) ◽  
pp. 487-513
Author(s):  
Nabil Kazi-Tani ◽  
Didier Rullière
Keyword(s):  
Random Vector ◽  
Necessary Conditions ◽  
Elliptical Distributions ◽  
Multivariate Distributions ◽  
New Class ◽  
The Law

AbstractIn this paper we investigate the link between the joint law of a d-dimensional random vector and the law of some of its multivariate marginals. We introduce and focus on a class of distributions, that we call projective, for which we give detailed properties. This allows us to obtain necessary conditions for a given construction to be projective. We illustrate our results by proposing some theoretical projective distributions, as elliptical distributions or a new class of distribution having given bivariate margins. In the case where the data does not necessarily correspond to a projective distribution, we also explain how to build proper distributions while checking that the distance to the prescribed projections is small enough.

scholarly journals Linear combinations of prime powers in binary recurrence sequences

2017 ◽  
Vol 13 (02) ◽  
pp. 261-271 ◽  
Author(s):  
Csanád Bertók ◽  
Lajos Hajdu ◽  
István Pink ◽  
Zsolt Rábai
Keyword(s):  
Linear Combination ◽  
The Other ◽  
Linear Recurrence ◽  
Linear Combinations ◽  
Other Hand ◽  
Sums Of Powers ◽  
Recurrence Sequences

We give finiteness results concerning terms of linear recurrence sequences having a representation as a linear combination, with fixed coefficients, of powers of fixed primes. On one hand, under certain conditions, we give effective bounds for the terms of binary recurrence sequences with such a representation. On the other hand, in the case of some special binary recurrence sequences, all terms having a representation as sums of powers of [Formula: see text] and [Formula: see text] are explicitly determined.

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

Theoretical analysis of ultraviolet spectroscopic studies on the feathering of cream in coffee

1989 ◽  
Vol 56 (5) ◽  
pp. 749-754 ◽  
Author(s):  
David A. Pink ◽  
Lucie Hamboyan ◽  
Helen Aboud
Keyword(s):  
Theoretical Analysis ◽  
Chlorogenic Acid ◽  
Linear Combination ◽  
Spectroscopic Studies ◽  
The Other ◽  
Ultraviolet Spectra ◽  
Spectral Bands

SummaryUltraviolet spectra of solutions of instant and filter coffees have been analysed as a linear combination of component Gaussian bands. We show that the ratio, R′, of two of these bands, one at 329 nm due almost entirely to chlorogenic acid, and the other at 272 nm due to a coffee component not appearing in the chlorogenic acid spectrum, is analogous to the ratio R (Hamboyan et al. 1989). The use of R which is easier to measure than R′ has therefore been justified on physical grounds, based on the existence of component spectral bands. Filter coffees appeared to exhibit behaviour similar to that of instant coffees.

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