On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Lague divergence
On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Lague divergence
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DOI：
10.1524/stnd.2005.23.2.117
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发表时间：
2005-02-01
影响因子：
1.5
通讯作者：
Schwingenschloegl, Udo
中科院分区：
文献类型：
--
作者：
Heinrich, Lothar;Pukelsheim, Friedrich;Schwingenschloegl, Udo
固定乘子法是将真实概率四舍五入到有理比例的过程，而圣莱格散度是对这一四舍五入步骤产生的累积误差的合理衡量。假设给定的概率是均匀分布的，我们证明了Sainte-Lague发散收敛于标准舍入乘子法所得到的Levy稳定分布。实现收敛的正规化常数以一种微妙的方式依赖于所使用的静态方法。
Stationary multiplier methods are procedures for rounding real probabilities into rational proportions, while the Sainte-Lague divergence is a reasonable measure for the cumulative error resulting from this rounding step. Assuming the given probabilities to be uniformly distributed, we show that the Sainte-Lague divergences converge to the Levy-stable distribution that obtains for the multiplier method with standard rounding. The norming constants to achieve convergence depend in a subtle way on the stationary method used.