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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), ...

Given a random variable x and a probability density function P(x), if there exists an h>0 such that M(t)=<e^(tx)> (1) for |t|<h, where <y> denotes the expectation value of y, ...

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 ...

The noncentral chi-squared distribution with noncentrality parameter lambda is given by P_r(x) = ...

The distribution with probability density function and distribution function P(x) = (ab^a)/(x^(a+1)) (1) D(x) = 1-(b/x)^a (2) defined over the interval x>=b. It is ...

A skewed distribution which is similar to the binomial distribution when p!=q (Abramowitz and Stegun 1972, p. 930). y=k(t+A)^(A^2-1)e^(-At), (1) for t in [0,infty) where A = ...

The distribution with probability density function and distribution function P(r) = (re^(-r^2/(2s^2)))/(s^2) (1) D(r) = 1-e^(-r^2/(2s^2)) (2) for r in [0,infty) and parameter ...

For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...

The score function u(theta) is the partial derivativeof the log-likelihood function F(theta)=lnL(theta), where L(theta) is the standard likelihood function. Defining the ...

If a random variable X has a chi-squared distribution with m degrees of freedom (chi_m^2) and a random variable Y has a chi-squared distribution with n degrees of freedom ...