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The operator tpartial/partialr that can be used to derive multivariate formulas for moments and cumulants from corresponding univariate formulas. For example, to derive the ...

The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, ...

The Maxwell (or Maxwell-Boltzmann) distribution gives the distribution of speeds of molecules in thermal equilibrium as given by statistical mechanics. Defining a=sqrt(kT/m), ...

The mode of a set of observations is the most commonly occurring value. For example, for a data set (3, 7, 3, 9, 9, 3, 5, 1, 8, 5) (left histogram), the unique mode is 3. ...

Let a set of random variates X_1, X_2, ..., X_n have a probability function P(X_1=x_1,...,X_n=x_n)=(N!)/(product_(i=1)^(n)x_i!)product_(i=1)^ntheta_i^(x_i) (1) where x_i are ...

Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As ...

The statistics h_(r,s,...) defined such that <h_(r,s,...)>=mu_rmu_s..., where mu_r is a central moment. These statistics generalize h-statistics and were originally called ...

The symmetric statistic k_(r,s,...) defined such that <k_(r,s,...)>=kappa_rkappa_s..., (1) where kappa_r is a cumulant. These statistics generalize k-statistic and were ...

The probability Q_delta that a random sample from an infinite normally distributed universe will have a mean m within a distance |delta| of the mean mu of the universe is ...

On a three-dimensional lattice, a random walk has less than unity probability of reaching any point (including the starting point) as the number of steps approaches infinity. ...