论文标题
随机变量及其应用的复杂功率均值的属性
Properties of complex-valued power means of random variables and their applications
论文作者
论文摘要
我们考虑了独立和相同分布的（I.I.D.）的功率手段。功率平均值是同质准算术平均值的一个例子。在某些条件下，与i.i.d的算术平均值相似的幂均值定理的限制定理。可集成的随机变量。我们的功能是，允许势力的发电机复杂价值，这使我们能够考虑整个实数中支持的随机变量的功率平均值。我们建立了I.I.D.权力平均值的综合性不可集成的随机变量和功率均值方差的极限定理。我们还将功率均值的行为视为功率的参数各不相同。对于凯奇分布的位置和尺度参数的关节，复杂值的功率平均值是公正的，坚强的，可靠的估计器。
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a homogeneous quasi-arithmetic mean. Under certain conditions, several limit theorems hold for the power mean, similar to the case of the arithmetic mean of i.i.d. integrable random variables. Our feature is that the generators of the power means are allowed to be complex-valued, which enables us to consider the power mean of random variables supported on the whole set of real numbers. We establish integrabilities of the power mean of i.i.d. non-integrable random variables and a limit theorem for the variances of the power mean. We also consider the behavior of the power mean as the parameter of the power varies. The complex-valued power means are unbiased, strongly-consistent, robust estimators for the joint of the location and scale parameters of the Cauchy distribution.
