APPROXIMATION OF PROBABILITY DISTRIBUTIONS BY CONVEX MIXTURES OF GAUSSIAN MEASURES
APPROXIMATION OF PROBABILITY DISTRIBUTIONS BY CONVEX MIXTURES OF GAUSSIAN MEASURES
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DOI：
10.1090/s0002-9939-10-10340-2
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发表时间：
2010-07-01
影响因子：
1
通讯作者：
Bacharoglou, Athanassia G.
中科院分区：
文献类型：
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作者：
Bacharoglou, Athanassia G.
设A(+)={a=(a(N))是布尔元，(p>；i)L(P)：A(N)>；0，for all(N)是N的一个元}，设{171是所有均值为有理数且方差为1/n(2)的正态分布的计数，a=1，2……我们证明了存在a是A(+)的一个元，使得在R中具有紧支集的连续概率密度函数可以同时用平均值1/Sigma(N)(j=1)a(J)Sigma(N)(j=1)a(J)Phi(J)逼近于L1和L范数。这类序列的集合是A(+)中的稠密G(Delta)集，并且包含一个稠密的正锥。
Let A(+) = {a = (a(n)) is an element of boolean AND(p>I) l(p) : a(n) > 0, for all(n) is an element of N} and let {171 be an enumeration of all normal distributions with mean a rational number and variance 1/n(2), a = 1,2 .... We prove that there exists an a is an element of A(+) such that that every probability density function, continuous, with compact support in R. can be approximated in L1 and L norm simultaneously by the averages 1/Sigma(n)(j=1)a(j) Sigma(n)(j=1) a(j)phi(j). The set of such sequences is a dense G(delta) set in A(+) and contains a dense positive cone.