Method for constructing Stieltjes classes for M-indeterminate probability distributions
Method for constructing Stieltjes classes for M-indeterminate probability distributions
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M-不确定概率分布的 Stieltjes 类构造方法
DOI：
10.1016/j.amc.2004.04.035
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Leonid Tolmatz
中科院分区：
文献类型：
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作者：
J. Stoyanov;Leonid Tolmatz
设F是一个密度为F的分布函数，具有任意正整数阶的有限矩，使得F的矩问题有一个非唯一解（F是m不定式）。我们正在寻找显式Stieltjes类ess ={fε=f[1+εh], ε∈[- 1,1]}的分布（这里以它们的密度表示）都与f具有相同的矩。我们提出了一个构造此类类的一般方法。然后，我们将该方法应用于描述对数正态分布、逆高斯分布和逻辑分布等常用分布的幂变换的m -不确定性。这里介绍的Stieltjes类是新的。我们还找到了一些特殊情况下的不相似指数的数值。
Let F be a distribution function with density f, finite moments of any positive integer order and such that the problem of moments for F has a nonunique solution (F is M-indeterminate). We are looking for explicit Stieltjes classesS={fε=f[1+εh], ε∈[−1,1]} of distributions (here in terms of their densities) all sharing the same moments as those of F. We suggest a general method for constructing such classes. Then we apply our method to describe the M-indeterminacy of power transformations of popular distributions such as lognormal, inverse Gaussian and logistic. The Stieltjes classes presented here are new. We also find numerical values of the index of dissimilarity for some particular cases.