The goal of the present paper is to expand already published works in the frame of＂Banded speed cosmology＂ （BSC）. In particular this paper gives validated values for physical quantities not so far investigated in ...The goal of the present paper is to expand already published works in the frame of＂Banded speed cosmology＂ （BSC）. In particular this paper gives validated values for physical quantities not so far investigated in previous publications, i.e., the number of individual physical entity in the universe, as well as the maximum value for acceleration. Validates values mean identical quantities from a numerical point of view obtained with different theoretical procedures, additionally compared with data based on NASA observations with Planck probe.展开更多
Although advanced statistical models have been proposed to fit complex data better,the advances of science and technology have generated more complex data,e.g.,Big Data,in which existing probability theory and statist...Although advanced statistical models have been proposed to fit complex data better,the advances of science and technology have generated more complex data,e.g.,Big Data,in which existing probability theory and statistical models find their limitations.This work establishes probability foundations for studying extreme values of data generated from a mixture process with the mixture pattern depending on the sample length and data generating sources.In particular,we show that the limit distribution,termed as the accelerated max-stable distribution,of the maxima of maxima of sequences of random variables with the above mixture pattern is a product of three types of extreme value distributions.As a result,our theoretical results are more general than the classical extreme value theory and can be applicable to research problems related to Big Data.Examples are provided to give intuitions of the new distribution family.We also establish mixing conditions for a sequence of random variables to have the limit distributions.The results for the associated independent sequence and the maxima over arbitrary intervals are also developed.We use simulations to demonstrate the advantages of our newly established maxima of maxima extreme value theory.展开更多
文摘The goal of the present paper is to expand already published works in the frame of＂Banded speed cosmology＂ （BSC）. In particular this paper gives validated values for physical quantities not so far investigated in previous publications, i.e., the number of individual physical entity in the universe, as well as the maximum value for acceleration. Validates values mean identical quantities from a numerical point of view obtained with different theoretical procedures, additionally compared with data based on NASA observations with Planck probe.
基金partially supported by NSF-DMS-1505367 and Wisconsin Alumni Research Foundation#MS N215758partially supported by National Science Foundation NSF-DMS-1505367 and NSFDMS-2012298.
文摘Although advanced statistical models have been proposed to fit complex data better,the advances of science and technology have generated more complex data,e.g.,Big Data,in which existing probability theory and statistical models find their limitations.This work establishes probability foundations for studying extreme values of data generated from a mixture process with the mixture pattern depending on the sample length and data generating sources.In particular,we show that the limit distribution,termed as the accelerated max-stable distribution,of the maxima of maxima of sequences of random variables with the above mixture pattern is a product of three types of extreme value distributions.As a result,our theoretical results are more general than the classical extreme value theory and can be applicable to research problems related to Big Data.Examples are provided to give intuitions of the new distribution family.We also establish mixing conditions for a sequence of random variables to have the limit distributions.The results for the associated independent sequence and the maxima over arbitrary intervals are also developed.We use simulations to demonstrate the advantages of our newly established maxima of maxima extreme value theory.
