The method of moments is an old statistical technique that fits parameters of a model by matching the average value of moments under the model with their average value over the data. Recently, approximate versions of this basic technique have been proposed in several diverse literatures including statistics, econometrics, population genetics, systems biology, ecology, epidemiology, and image te...

Politano and Pouquet’s law, a generalization of Kolmogorov’s four-fifths law to incompressible MHD, makes it possible to measure the energy cascade rate in incompressible MHD turbulence by means of third-order moments. In hydrodynamics, accurate measurement of thirdorder moments requires large amounts of data because the probability distributions of velocity-differences are nearly symmetric and...

We present numerical and analytical results for a stochastic representation of immiscible flow in a heterogeneous reservoir. Using a perturbation method, we derive equations of statistical moments to second order in the standard deviation of log permeability. We allow these moments to depend on location, hence the common assumption of statistical homogeneity (stationarity) does not apply. This ...

Monte Carlo methods and simulation are often used to estimate the mean, variance, and higher order statistical moments of circuit properties like delay and power. The main issues with Monte Carlo methods are the required long run time and the need for prior detailed knowledge of the distribution of the variations. Additionally, most of available circuit simulation tools can run Monte Carlo anal...

Description The package implements the statistical theory of L-moments in R including L-moment estimation, probability-weighted moment estimation, parameter estimation for numerous familiar and not-so-familiar distributions, and L-moment estimation for the same distributions from the parameters. L-moments are derived from the expectations of order statistics and are linear with respect to the p...

For a discrete distribution in Rd on a finite support D probabilities and moments are algebraically related. If there are n = |D| support points then there are n probabilities p(x), x ∈ D and n basic moments. By suitable interpolation of the probabilities using a Gröbner basis method, high order moments can be express linearly in terms of n basic moments. A main result is that high order cumula...

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...