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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 ...

A simple point process (or SPP) is an almost surely increasing sequence of strictly positive, possibly infinite random variables which are strictly increasing as long as they ...

A correction to a discrete binomial distribution to approximate a continuous distribution. P(a<=X<=b) approx P((a-1/2-np)/(sqrt(np(1-p)))<=z<=(b+1/2-np)/(sqrt(np(1-p)))), ...

Loess local regression is a nonparametric technique for describing bivariate relationships where the functional form is not known in advance.

The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j with sample size N, the midrange of the random sample is defined by MR=1/2(Y_1+Y_N) (Hogg and Craig ...

The positive predictive value is the probability that a test gives a true result for a true statistic. The negative predictive value is the probability that a test gives a ...

A statistical distribution in which the variates occur with probabilities asymptotically matching their "true" underlying statistical distribution is said to be random.

A statistical test making use of the statistical ranks of data points. Examples include the Kolmogorov-Smirnov test and Wilcoxon signed rank test.

Given two distributions Y and X with joint probability density function f(x,y), let U=Y/X be the ratio distribution. Then the distribution function of u is D(u) = P(U<=u) (1) ...