There are two approaches to adequately describe a sample sediment size frequency distribution in terms of four descriptive parameters (Krumbein and Pettijohn, 1938). These are used to distinguish either the mode of transportation or the environment of deposition of a sediment. The most mathematically elegant method of describing the complete frequency distribution is by the statistical moment measurements. Since most grain size distributions are approximately normal (or Gaussian ) when their φ size is plotted on an arithmetic scale, conventional moment statistics can be used to characterize an individual sample.
The mathematical expectation of a variable [g(x)] related to x is: E(x) = Σg(x)f(x), where f(x) is the probability function at x and the summation extends over the entire range of g(x) (Kreyzig, 1970). If g(x) = x r or E(x r) = Σx r f(x) = m r, this is called the r th moment about the origin of the distribution of the random variable x. The term momentis borrowed from...
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Brenninkmeyer, B.M. (1982). Moment measures . In: Beaches and Coastal Geology. Encyclopedia of Earth Sciences Series. Springer, New York, NY. https://doi.org/10.1007/0-387-30843-1_287
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