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P(Z)=Z/(sigma^2)exp(-(Z^2+|V|^2)/(2sigma^2))I_0((Z|V|)/(sigma^2)), where I_0(z) is a modified Bessel function of the first kind and Z>0. For a derivation, see Papoulis ...

A specification of elements in a list as a list of pairs giving the element and number of times it occurs in a run. For example, given the list ...

Let there be x successes out of n Bernoulli trials. The sample proportion is the fraction of samples which were successes, so p^^=x/n. (1) For large n, p^^ has an ...

Sample size is the number of observations in a sample (Evans et al. 2000, p. 16). It is commonly denoted n or N.

In random number computation, a seed is an initial number used as the starting point in a random number generating algorithm. In a dynamical system, a seed is a starting ...

A test for determining the probability that a given result could not have occurred by chance (its significance).

Let H be a two-dimensional distribution function with marginal distribution functions F and G. Then there exists a copula C such that H(x,y)=C(F(x),G(y)). Conversely, for any ...

A moving average may generate an irregular oscillation even if none exists in the original data.

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...