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The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

A generalization of the Wilcoxon rank sum test.

Given a series of positive terms u_i and a sequence of finite positive constants a_i, let rho=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)). 1. If rho>0, the series converges. ...

A nonparametric alternative to the two-sample t-test.

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

The limit test, also sometimes known as the nth term test, says that if lima_n!=0 or this limit does not exist as n tends to infinity, then the series suma_n does not ...

A statistical test in which assumptions are made about the underlying distribution of observed data.

The Wilcoxon test statistic is equivalent to the T_+ statistic in the Wilcoxon signed rank test (Kanji 1999).

The compositeness test consisting of the application of Fermat's little theorem.

Let u_k be a series with positive terms and suppose rho=lim_(k->infty)(u_(k+1))/(u_k). Then 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series diverges. ...