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Noncentral quadratic forms of the skew elliptical variables 总被引:1,自引:0,他引:1
In this paper the quadratic forms in the skew elliptical variables are studied. A family of the noncentral generalized Dirichlet distributions is introduced and their distribution functions and probability density functions are obtained. The moment generating functions of the quadratic forms in the skew normal variables are obtained. Sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the noncentral generalized Dirichlet distributions are obtained. This leads to the noncentral Cochran's Theorem for the skew normal distribution. 相似文献
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Barry C. Arnold Enrique Castillo JosMaría Sarabia 《Statistics & probability letters》1994,20(5):353-354
If X is a k-dimensional random vector, we denote by X(i) the vector X with coordinate i deleted and by X(i,j) the vector X with coordinates i and j deleted. If for each i the conditional distribution of Xi given X(i) = x(i) is univariate normal for each x(i)
K−1 and if for each i, j the conditional distribution of Xi given X(i,j) = x(i,j) is univariate normal for each x(i,j)
k−2 then it is shown that X has a classical k-variate normal distribution. 相似文献
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本文采用不同以往的方法;对正态定限(Orthant)概率积分施行线性变换与极坐标变换;得到了一个新的递推公式,使积分重数至少降低了3重;并推导了四维正态定限概率的表达式,这对进行数值计算是十分有意义的. 相似文献
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Kenneth Lange Janet S. Sinsheimer 《Journal of computational and graphical statistics》2013,22(2):175-198
Abstract Maximum likelihood estimation with nonnormal error distributions provides one method of robust regression. Certain families of normal/independent distributions are particularly attractive for adaptive, robust regression. This article reviews the properties of normal/independent distributions and presents several new results. A major virtue of these distributions is that they lend themselves to EM algorithms for maximum likelihood estimation. EM algorithms are discussed for least Lp regression and for adaptive, robust regression based on the t, slash, and contaminated normal families. Four concrete examples illustrate the performance of the different methods on real data. 相似文献
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The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic mappings and normal holomorphic mappings of several complex variables into p^N (C) for continuously moving hyperplanes in pointwise general position. The main results are also true for continuously moving hypersurfaces in pointwise general position. Examples are given to show the sharpness of the results. 相似文献
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A multiresolution analysis of a curve is normal if
each wavelet detail vector with respect to a certain subdivision
scheme lies in the local normal direction. In this paper we study
properties such as regularity, convergence, and stability of a
normal multiresolution analysis. In particular, we show that these
properties critically depend on the underlying subdivision scheme
and that, in general, the convergence of normal multiresolution
approximations equals the convergence of the underlying subdivision
scheme. 相似文献
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群G的一个L-模糊正规子群A的陪集做成的群G/A与群G的一个商群是自然同构的。如果f:G→G’是群的满同态,则G’的L-模糊正规子群做成的群与G的在f的核上取定值的L-模糊正规子群做成的群之间存在一个保序的双射。 相似文献
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Pascal Massart 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):991
The optimal coupling between a variable with the Bin(n,1/2) distribution and a normal random variable lies at the heart of the proof of the KMT Theorem for the empirical distribution function. Tusnády's Lemma (published in 1977 in his dissertation and in Hungarian) provides an inequality with explicit absolute constants which says that for this coupling, the distance between the random variables remains bounded in probability. In the appendix of a joint work with Jean Bretagnolle (1989), we have proposed a proof of Tusnády's Lemma which though elementary is highly technical and considered as rather obscure, at least this is what we have understood from several conversations with motivated readers. The purpose of this paper is to provide an alternative proof which is still based on elementary computations but which we hope to be simpler and more illuminating. This new proof also leads to a slight improvement on the original result in terms of constants. 相似文献
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对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测.本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测. 相似文献
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R. S. Srivastava 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(5):832-842
The diffraction of normal shock with yawed wedges of small angles have been considered in this paper. Vorticity distribution
of the fluid particle over the diffracted shock has been determined for several Mach numbers of the shock wave. The Mach reflection
effects have also been investigated when the bend is concave to the flow. 相似文献
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Wolfgang Stadje 《Operations Research Letters》1997,20(5):229-235
It is proved that a certain kind of randomly discounted random sums is asymptotically normal as the discount constant tends to zero. For replaceable systems with random lifetime, these sums represent the total discounted cost of policies of the age-replacement type; other applications to queueing and related areas are also indicated. 相似文献
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证明了从C~n的一个区域到P~N(C)中的多复变全纯映射族为正规族的一个充要条件.这个充要条件与P~N(C)中的逐点处于一般位置的连续移动超平面族有关.证明的主要方法来自于微分方程. 相似文献
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设$X_1,X_2,\cdots,X_n$和$X^*_1,X^*_2,\cdots,X^*_n$分别服从正态分布$N(\mu_i,\sigma^2)$和$N(\mu^*_i,\sigma^2)$,以$X_{(1)}$,$X^*_{(1)}$分别表示$X_1,\cdots,X_n$和$X^*_1,\cdots,X^*_n$的极小次序统计量,以$X_{(n)}$, $X^*_{(n)}$分别表示$X_1,\cdots,X_n$和$X^*_1,\cdots$,$X^*_n$的极大次序统计量. 我们得到了如下结果:(i)\,如果存在严格单调函数$f$使得$(f(\mu_{1}),\cdots,f(\mu_{n}))\succeq_{\text{m}}$ $(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,且$f'(x)f'(x)\!\geq\!0$, 则$X_{(1)}\!\leq_{\text{st}}\!X^*_{(1)}$;(ii)\,如果存在严格单调函数$f$使得$(f(\mu_{1})$,$\cdots,f(\mu_{n}))\succeq_{\text{m}}(f(\mu^{*}_{1}),\cdots,f(\mu^{*}_{n}))$,且$f'(x)f'(x)\leq 0$, 则$X_{(n)}\geq_{\text{st}}X^*_{(n)}$.(iii)\,设$X_{1},X_{2},\cdots,X_{n}$和\, $X^*_{1},X^*_{2},\cdots,X^*_{n}$分别服从正态分布$N(\mu,\sigma_i^2)$和$N(\mu,\sigma_i^{*2})$,若$({1}/{\sigma_{1}},\cdots,{1}/{\sigma_{n}})\succeq_{\text{m}}({1}/{\sigma^{*}_{1}},\cdots,{1}/{\sigma^{*}_{n}})$,则有$X_{(1)}\leq_{\text{st}}X^*_{(1)}$和$X_{(n)}\geq_{\text{st}}X^*_{(n)}$同时成立. 相似文献
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The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the
complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using a normal
holonomy approach. Indeed, we explain how these submanifolds can be regarded as the unique complex orbits of the (projectivized)
isotropy representation of an irreducible Hermitian symmetric space. Moreover, we show how these important submanifolds are
related to other areas of mathematics and theoretical physics. Finally, we state a conjecture about the normal holonomy group
of a complete and full complex submanifold of the complex projective space.
Research partially supported by GNSAGA (INdAM) and MIUR of Italy. 相似文献
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As a new statistician, W.F. Sheppard wrote a series of letters to the leading statistician of the day, Karl Pearson, for his advice. Written a century ago and spanning three decades, the letters provide a glimpse into the development of two significant contributions to statistics: the normal probability tables, and the corrections of moment estimates. Sheppard's normal probability tables were the first set of modern tables for the standard normal distribution and have been widely used since the twentieth century. We provide an examination of the statistical research carried out by Sheppard and Pearson in the context of their correspondence. 相似文献
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Hichem Sellami 《Mathematical Programming》1998,82(3):317-337
In this paper, we present a continuation method for solving normal equations generated byC
2
functions and polyhedral convex sets. We embed the normal map into a homotopyH, and study the existence and characteristics of curves inH
1(0) starting at a specificd point. We prove the convergence of such curves to a solution of the normal equation under some conditions on the polyhedral convex setC and the functionf. We prove that the curve will have finite are length if the normal map, associated with the derivative df(·) and the critical coneK, is coherently oriented at each zero of the normal mapf
c
inside a certain ball of
n
. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This research was performed at the Department of Industrial Engineering, University of Wisconsin-Madison, Madison, WI, USA. 相似文献