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Two figures are homothetic if they are related by a dilation (a dilation is also known as a homothecy). This means that the connectors of corresponding points are concurrent ...

The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio (Courant and Robbins 1996, p. 172; Durell 1928, p. 73), ...

Given a geometric sequence {a_1,a_1r,a_1r^2,...}, the number r is called the common ratio associated to the sequence.

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. ...

Let there be N_i observations of the ith phenomenon, where i=1, ..., p and N = sumN_i (1) y^__i = 1/(N_i)sum_(alpha)y_(ialpha) (2) y^_ = 1/Nsum_(i)sum_(alpha)y_(ialpha). (3) ...

The Sharpe ratio is a risk-adjusted financial measure developed by Nobel Laureate William Sharpe. It uses a fund's standard deviation and excess return to determine the ...

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) ...

A quantity used to test nested hypotheses. Let H^' be a nested hypothesis with n^' degrees of freedom within H (which has n degrees of freedom), then calculate the maximum ...

The Mills ratio is defined as m(x) = 1/(h(x)) (1) = (S(x))/(P(x)) (2) = (1-D(x))/(P(x)), (3) where h(x) is the hazard function, S(x) is the survival function, P(x) is the ...