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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 ...

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 ...

There are a number of point processes which are called Hawkes processes and while many of these notions are similar, some are rather different. There are also different ...

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, ...

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, ...

A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...