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In mathematics, the ratio test is a test (or "criterion") for the convergence of a series =, where each term is a real or complex number and a n is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
In practice, the likelihood ratio is often used directly to construct tests — see likelihood-ratio test.However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this, one considers algebraic manipulation of the ratio to see if there are key statistics in it related to the size of the ratio (i.e. whether a large ...
The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals.
English: A plot showing how the ratio test test is proven in the convergent case. Given a sequence like the blue one, for which the ratio of adjacent terms | a n + 1 / a n | {\displaystyle |a_{n+1}/a_{n}|} converges to L < 1, we identify a ratio r = (L+1)/2 and show that for large enough n the sequence is dominated by the simple geometric ...
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The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not ...
Even though the quick bread batter only asked for 2 tablespoons of oil and included the same amount of bananas as most of our Test Kitchen’s signature banana bread recipes, this ended up tender ...
A cheat sheet (also cheatsheet) or crib sheet is a concise set of notes used for quick reference. Cheat sheets were historically used by students without an instructor or teacher's knowledge to cheat on a test or exam. [1] In the context of higher education or vocational training, where rote memorization is not as important, students may be ...