Franck, W. E.
and Hanson, D. L.
, Some results giving rates of convergence in the law of large numbers for weightedsums of independent variables,.
Trans. Amer. Math. Soc.
Authors:Han-Ying Liang, Jong-Il Baek, and Josef Steinebach
Let X1, X2,… be independent, but not necessarily identically distributed random variables in the domain of attraction of a stable law with index 0<a<2. This paper uses Mn=max 1?i?n|Xi| to establish a self-normalized law of the iterated logarithm (LIL) for partial sums. Similarly self-normalized increments of partial sums are studied as well. In particular, the results of self-normalized sums of Horváth and Shaounder independent and identically distributed random variables are extended and complemented. As applications, some corresponding results for self-normalized weighted sums of iid random variables are also concluded.
Authors:J. A. García, Rosa Rodriguez-Sánchez, and J. Fdez-Valdivia
overall prestige as the normalized weightedsum of the contribution of each one journal to the overall prestige as follows:
Definition 1 A measure of the overall prestige R of journals with ranking score above a threshold z , for a
Authors:J. A. García, Rosa Rodriguez-Sánchez, J. Fdez-Valdivia, Daniel Torres-Salinas, and Francisco Herrera
the multidimensional prestige of influential fields at the university as the normalized weightedsum of the field contribution to the overall prestige as follows:
Given a configuration of dimension