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The Wiener sausage of radius a>0 is the random process defined by W^a(t)= union _(0<=s<=t)B_a(beta(s)) where here, beta(t) is the standard Brownian motion in R^d for t>=0 and ...

The probability of getting at least one "6" in four rolls of a single 6-sided die is 1-(5/6)^4 approx 0.5177, (1) which is slightly higher than the probability of at least ...

The correlation coefficient, sometimes also called the cross-correlation coefficient, Pearson correlation coefficient (PCC), Pearson's r, the Perason product-moment ...

The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

The determination of a test for the equality of means for two normal distributions with different variances given samples from each. There exists an exact test which, ...

The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population. The Gini coefficient is most easily calculated ...

Given a sequence of values {a_k}_(k=1)^n, the high-water marks are the values at which the running maximum increases. For example, given a sequence (3,5,7,8,8,5,7,9,2,5) with ...

Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps. 1. ...

A statistic which assigns a single number to several individual statistics in order to quantify trends. The best-known index in the United States is the consumer price index, ...