Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-11-17
Physics
Condensed Matter
Statistical Mechanics
20 pages, 5 figures, accepted in Physica A
Scientific paper
10.1016/j.physa.2009.11.018
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. Applications to the statistical characterization of raw data and in the representation of both random variables and vectors are provided, showing that the good numerical convergence makes the proposed approach a good and reliable tool also for practical data analysis.
Cottone Giulio
Metzler Ralf
Paola Mario Di
No associations
LandOfFree
Fractional calculus approach to the statistical characterization of random variables and vectors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fractional calculus approach to the statistical characterization of random variables and vectors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractional calculus approach to the statistical characterization of random variables and vectors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-650631