Rationalizing the Study of Moments
Collection OverviewThis is part of the moments math collection.
Several terms need to be clariﬁed mathematically to appreciate the large sets of data which are typical of experiments. Their relevance lies in the fact that extrapolation of mathematical terms is easier than quantifying in words, more complex systems. Where applicable, general interpretations are indicated, however, most of the discussion of these terms is left to the second chapter; where speciﬁc chemical engineering applications are enumerated.
We seek to ﬁrst place on an mathematical footing, the easily grasped concepts of various experimental terms (e.g., random variables). Subsequently it is shown via simple mathematical constructs, how prior concepts may be generalized (moments). Finally the utility of these constructs is explored brieﬂy in context of predictive ability and the systematic treatment of non-intuitive results.
Elementary set theory is a pre-assumed, and certain aspects require a level of mathematical rigor best obtained by a familiarity with the rigidity of technical definitions.
The apparent abstractness of this section is offset by the utility of having mathematical concepts accessible without being tied to physical examples. (i.e., allowing concepts to retain a logical purity.)
Additionally, the study of moments forms the cornerstone of a generalized study of statistics in it’s entirety. Recognizing this, focus has been given to mainly the initial and central moments of single random variables in this treatise.
This collection is largely inspired from Bronshtein et al. (2015), Polyanin and Manzhirov (2006) and Polyanin and Chernoutsan (2010).
This series consists of:
Bronshtein, I.N., K.A. Semendyayev, G. Musiol, and H. Mühlig. 2015. Handbook of Mathematics. Springer Berlin Heidelberg. https://books.google.co.in/books?id=5L6BBwAAQBAJ.
Polyanin, A.D., and A.I. Chernoutsan. 2010. A Concise Handbook of Mathematics, Physics, and Engineering Sciences. CRC Press. https://books.google.co.in/books?id=ejzScufwDRUC.
Polyanin, A.D., and A.V. Manzhirov. 2006. Handbook of Mathematics for Engineers and Scientists. Taylor & Francis. https://books.google.co.in/books?id=ge6nk9W0BCcC.